Mathematics High School

Verify 1) x³+y³=(x+y)(x²-xy+y²)
2) x³-y³=(x-y)(x²+xy+y²)
using some non-zero positive integers and check by actual multiplication. can you call these as identities? ​

Answers

Answer 1
To Prove & verify that :

x³ + y³ = (x + y)(x² - xy + y²)

x³ - y³ = (x - y)(x² + xy + y²).

Proof for 1st Identity :

★ x³ + y³ = x (x² - xy + y²) + y(x² - xy + y²)

⟶ x³ + y³ = x³ - x²y + xy² + x²y - xy² + y³

⟶ x³ + y³ = x³ + y³

Proof for 2nd identity :

★ x³ - y³ = x(x² + xy + y²) - y(x² + xy + y²)

⟶ x³ - y³ = x³ + x²y + xy² - x²y - xy² - y³

⟶ x³ - y³ = x³ - y³

For example,

Let us assume that,

x = 1

y = 2

So,

✯ x³ + y³ = 1³ + 2³

⟹ (x + y)(x² - xy + y²) = 1 + 8

⟹ (1 + 2)(1² - (1)(2) + 2²) = 9

⟹ 3 * (1 - 2 + 4) = 9

⟹ 3 * 3 = 9

⟹ 9 = 9

✯ x³ - y³ = 1³ - 2³

⟹ (1 - 2) * (1² + (1)(2) + 2²) = 1 - 8

⟹ ( - 1) * (1 + 2 + 4) = - 7

⟹ ( - 1) * (7) = - 7

⟹ - 7 = - 7

Thus , they can be called as identities/formulae as they are very useful in finding the value of a certain equation or an expression easily.

I hope it will help you.

Regards.

Related Questions

A department store buys 200 shirts at a cost of $1,600 and sells them at a selling price of $10
each, Find the percent markup.

Answers

It would be 160% I think

Tina recorded the number of calories she burned during a bike ride. The graph shows Tina’s calories burned, y, after x hours. If Tina rode her bike at a constant rate for the first three hours, what was Tina’s average calories burned, in calories per hour, between hour 0 and hour 3?

Answers

Answer:

the answer is B because 2x3 is ainzqwndwqncjnjqanc2ejn2qncb

Step-by-step explanation:

400 per hour was Tina's average calorie burn per hour between hours 0 and 3 if she rode her bike at a steady speed for the first three hours.

Given that,

Tina kept track of the calories she expended while riding her bike. After x hours, the graph displays Tina's calories burned, y.

We have to find what was Tina's average calorie burn per hour between hours 0 and 3 if she rode her bike at a steady speed for the first three hours.

What is a graph?

A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics. The relationships between two or more objects are often shown by the points on a graph.

Therefore, 400 per hour was Tina's average calorie burn per hour between hours 0 and 3 if she rode her bike at a steady speed for the first three hours.

To learn more about hours visit: https://brainly.com/question/13533620

#SPJ2

Mr. Garcia wants to leave a 15% tip to his server at Applebee's. If his total was $75, how much would his total be including the tip? *

$11.25
$90.00
$86.25
$75.15

Answers

A 11.25
Anything else is to much

Multiply. Enter the product in simplest form.
2/7 x 4/5

Answers

The answer is 8/35 ;)

expand (2a +36) (2a-3b​

Answers

Use the binomial expansion theorem to find each term. The binomial theorem states
(
a
+
b
)
n
=
n
∑
k
=
0

n
C
k
⋅
(
a
n
−
k
b
k
)
(
a
+
b
)
n
=
∑
k
=
0
n
⁡
n
C
k
⋅
(
a
n
-
k
b
k
)
.
3
∑
k
=
0

3
!
(
3
−
k
)
!
k
!
⋅
(
2
a
)
3
−
k
⋅
(
−
3
b
)
k
∑
k
=
0
3
⁡
3
!
(
3
-
k
)
!
k
!
⋅
(
2
a
)
3
-
k
⋅
(
-
3
b
)
k
Expand the summation.
3
!
(
3
−
0
)
!
0
!
⋅
(
2
a
)
3
−
0
⋅
(
−
3
b
)
0
+
3
!
(
3
−
1
)
!
1
!
⋅
(
2
a
)
3
−
1
⋅
(
−
3
b
)
+
3
!
(
3
−
2
)
!
2
!
⋅
(
2
a
)
3
−
2
⋅
(
−
3
b
)
2
+
3
!
(
3
−
3
)
!
3
!
⋅
(
2
a
)
3
−
3
⋅
(
−
3
b
)
3
3
!
(
3
-
0
)
!
0
!
⋅
(
2
a
)
3
-
0
⋅
(
-
3
b
)
0
+
3
!
(
3
-
1
)
!
1
!
⋅
(
2
a
)
3
-
1
⋅
(
-
3
b
)
+
3
!
(
3
-
2
)
!
2
!
⋅
(
2
a
)
3
-
2
⋅
(
-
3
b
)
2
+
3
!
(
3
-
3
)
!
3
!
⋅
(
2
a
)
3
-
3
⋅
(
-
3
b
)
3
Simplify the exponents for each term of the expansion.
1
⋅
(
2
a
)
3
⋅
(
−
3
b
)
0
+
3
⋅
(
2
a
)
2
⋅
(
−
3
b
)
+
3
⋅
(
2
a
)
⋅
(
−
3
b
)
2
+
1
⋅
(
2
a
)
0
⋅
(
−
3
b
)
3
1
⋅
(
2
a
)
3
⋅
(
-
3
b
)
0
+
3
⋅
(
2
a
)
2
⋅
(
-
3
b
)
+
3
⋅
(
2
a
)
⋅
(
-
3
b
)
2
+
1
⋅
(
2
a
)
0
⋅
(
-
3
b
)
3
Simplify each term.
Tap for more steps...
8
a
3
−
36
a
2
b
+
54
a
b
2
−
27
b
3
8
a
3
-
36
a
2
b
+
54
a
b
2
-
27
b
3

b) Simplify the expression (V7 + 3) square 2
​

Answers

V*7+3*v7+3 I’m not sure so I might be wrong

Answer:

[tex]49v^{2} +42v+9[/tex]

Step-by-step explanation:

First, let me say, I'm not sure what exactly the equation is because it's worded weirdly, but I'm assuming it's [tex](7v+3)^{2}[/tex].

(7v+3)(7v+3) [[tex]7v+3^{2}[/tex] is the same as (7v+3)(7v+3).]

[tex]49v^{2} +42v+9[/tex] [When you multiply them, this is the product.]

This is as far as you can simplify without knowing the value of v as far as I know.

Aubrey's dinner cost $85 She tips the waitstaff 30% for excellent service

Answers

Answer:

The total amount she paid would be $105.50.

Answer:

25.5 is the tip -- 110.50 is the total bill.

Step-by-step explanation:

You would calculate .30 (move the decimal over twice to switch from a percentage to a decimale) multiplied with 85 and this gives you 25.5.

85 * .3 = 25.5

Depending on the rest of the question, I added the tip to the amount of the dinner cost to obtain the total bill. You will need to see what the rest of the question is in order to verify which answer you are looking for.

what's 4 divided by 5 as a fraction ​

Answers

Answer:

four fifths because if you divided 4 by 5 is 0.8 and that equals four fifths

4. What is the solution of the proportion 3 16 = 9 y ?

Answers

answer:

5.33333333333

On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is LaTeX: t=\frac{1}{500}dt=1500d. How long will it take the airplane to travel 800 miles?

Answers

Answer:

1.6hours

Step-by-step explanation:

We know that Speed= distance/ time

But from the question, An equation relating the distance traveled in miles d to the number of hours flying t is t= 1/500d.

And the distance is given as 800 miles

Then, what we need is to substitute the given Distance into the equation of time.

t= 1/500d. Where d= 800 miles

t= (1/500) × 800 miles

t= 800 miles/500

t= 1.6hours

Hence, it will take the airplane to travel 800 miles , 1.6hours

Find the standard form for the equation of the line which
passes through the point (9,-46) and which has a
y-intercept of – 1.

Answers

Answer: Well I believe the answer is Y= x - 55

Step-by-step explanation:Hope that works :)

A speedboat, at full throttle, can go 65.0 miles in 1.5 hours. What is the average speed of the boat?

Answers

the average speed is about 40

Neuma has a container that held 9/54 of a kilogram of rainbow sprinkles she divided the sprinkles Evenly to put on top of the 9 servings of ice cream that she was making for her friends at the sleepover.To determine the weight of each serving neuma performed the calculations below she concluded that each serving weighs 1/6 of a kilogram. What is Neumas error?

Answers

Answer:

c. neuma should have only divided 9 by 9, not 54 by 9.

Step-by-step explanation:

Neuma had a container that held 9/54 of a kilogram of rainbow sprinkles. she divided the sprinkles evenly to put on top of the 9 servings of ice cream that she was making for her friends at the sleepover. to determine the weight of each serving, neuma performed the calculations below. she concluded that each serving weighs 1/6 of a kilogram. what is neuma’s error?

a. neuma should have multiplied by 54, not divided.

b. neuma should have multiplied by 9, not divided.

c. neuma should have only divided 9 by 9, not 54 by 9.

d. neuma should have only divided 54 by 9, not 9 by 9

Neuma's calculation

9/54

= 1/6

Kilogram of rainbow sprinkles = 9/54

Ice cream servings = 9

Correct calculation

Weight of each servings = total weight / number of servings

= 9 / 54 ÷ 9

= 9 / 54 × 1 / 9

= 1 / 54

Each servings = 1/54 kilogram

c. neuma should have only divided 9 by 9, not 54 by 9.

Answer:

c

Neuma should have only divided 9 by 9, not 54 by 9.

g(x) = -4(x + 3)(4x - 2)

Answers

X1=-3 X2=1/2 i think that’s the answer

Mr. Lowell has one of the most impressive antique toy collections in the United States, and he plans to distribute all 34,083 toys in his collection evenly to 21 different museums. How many toys will each museum get?

​

Answers

You have to divide 34,083 by 21 which gives you 1,623. So each museum will get 1,623 toys each.

Andy is scuba diving. He starts at sea level and then descends 10 feet in 212 minutes. Part A How would you represent Andy's descent as a unit rate? Express your answer as an integer. Enter your answer in the box. feet per minute Part B If he continues at this rate, where will Andy be in relation to sea level after 6 minutes? feet

Answers

Answer:

A. 4 feet per minute

B. 24 feet

Step-by-step explanation:

Given that: distance = 10 feet

                   time = 2 1/2 minutes = 2.5 minutes

A. The descent rate is the speed with which an object descends with respect to a reference point or plane.

Speed is the rate of the distance moved to time taken.

speed = [tex]\frac{distance}{time}[/tex]

           = [tex]\frac{10}{2.5}[/tex]

           = 4 feet/minute

Andy's descent is 4 feet/minute.

B. If he continues at this rate, his distance in relation to sea level after 6 minutes would be;

speed = [tex]\frac{distance}{time}[/tex]

4 = [tex]\frac{distance}{6}[/tex]

distance = 4 x 6

              = 24 feet

Thus, Andy would be at 24 feet in relation to sea level after 6 minutes.

To which subsets of numbers does 30/15 belong ?

Answers

30/15 = 2

Since 2 is a natural number, a whole number and an integer, so is 30/15.

Solve proportion 2/4.5=t/0.5

Answers

0.2 or 2/9 in fraction form I believe.

Given m 1= 65, find the measure of each missing angle.Givd your reasoning

Answers

Answer:

Step-by-step explanation:

Given:

m∠1 = 65°

Since. ∠1 and ∠2 are the angles of linear pair,

m∠1 + m∠2 = 180°

65° + m∠2 = 180°

m∠2 = 115°

m∠1 = m∠3 [Vertical angles]

m∠3 = 115°

Since, ∠1 and ∠4 is the linear pair of angles,

m∠1 + m∠4 = 180°

65° + m∠4 = 180°

m∠4 = 180 - 65 = 115°

m∠4 + m∠5 = 180° [Consecutive interior angles between the parallel lines]

115° + m∠5 = 180°

m∠5 = 180° - 115° = 65°

m∠5 + m∠6 = 180° [Linear pair of angles]

65° + m∠6 = 180°

m∠6 = 115°

m∠5 = m∠7 [Vertical angles]

m∠5 = m∠7 = 65°

m∠6 = m∠8 [Vertical angles]

m∠6 = m∠8 = 115°

Which inequality matches the graph shown?

Answers

Answer:

I am pretty sure it is x>8 which is B.

Step-by-step explanation:

I’m one hundred percent positive it’s B because if it’s open the aren’t less then or equivalent to or greater than or equivalent to

Could someone show me how to do this?

Answers

Step-by-step explanation:

b - no:of students on bus

V - " " on van

so the eqtn is

12v+10b=698

14v+2b=244

so when you solve these two eqtns you get

V=9

b=59

How do I solve |x-1|-1.4 = 6.2

Answers

Answer:

x1= -6.6   x2= 8.6

Step-by-step explanation:

Answer:

x1= -6.6, x2= 8.6

Step-by-step explanation:

|x-1|-1.4=6.2

|x-1|=6.2+1.4

|x-1|= 7.6

x-1=7.6 or x-1= -7.6

x= 8.6 and x= -6.6

A bag weighing 80 N rests on a horizontal surface. The coefficient of static friction between the bag and the surface is 0.4, and the coefficient of kinetic friction is 0.2. What minimum horizontal force must be applied to keep the bag moving at constant velocity once it has started to move?

Answers

Answer:

The minimum horizontal force that must be applied to keep the bag moving  at constant velocity once it has started to move is 16 newtons.

Step-by-step explanation:

According to the First and Second Newton's Laws, an object has net force of zero when it is at rest or moves at constant velocity. Given that bag rests on a horizontal surface, the equation of equilibrium is:

[tex]\Sigma F = P - f = 0[/tex] (Eq. 1)

Where:

[tex]P[/tex] - Horizontal force exerted on the bag, measured in newtons.

[tex]f[/tex] - Kinetic friction force, mesured in newtons.

From (Eq. 1), we get that horizontal force is:

[tex]P = f[/tex]

On the case of a horizontal surface, normal force exerted from ground on the bag and kinetic friction force is:

[tex]f = \mu_{k}\cdot W[/tex] (Eq. 2)

Where:

[tex]\mu_{k}[/tex] - Kinetic coefficient of friction, dimensionless.

[tex]W[/tex] - Weight of the bag, measured in newtons.

Then we eliminate kinetic friction force by equalizing (Eqs. 1, 2):

[tex]P = \mu_{k}\cdot W[/tex]

If we know that [tex]\mu_{k} = 0.2[/tex] and [tex]W = 80\,N[/tex], then the horizontal force that must be applied to is:

[tex]P =0.2\cdot (80\,N)[/tex]

[tex]P = 16\,N[/tex]

The minimum horizontal force that must be applied to keep the bag moving  at constant velocity once it has started to move is 16 newtons.

not really an academic subject lol just a stoopid inquiry
.
.
does anyone else stay up super late even if they're tired? like you haven't "completed" your day yet. just me?... TT_TT pls help

(my sleep schedule is very messed up) :,)

Answers

Answer:

Yes me too! Except I watch movies because I have a feeling they won't be there tomorrow lol

Step-by-step explanation:

What is the slope line through (0,4) and (3,2)?

Answers

Answer:

The answer is -2/Trust

Step-by-step explanation:

Answer:

Its D 100%

Step-by-step explanation:

What is the remainder when 69,694 is divided by 93?
​

Answers

Answer:

37

hope this helps :3

37 is the remainder when 69,694 is divided by 93

What is Division?

A division is a process of splitting a specific amount into equal parts.

We have to find the remainder when 69,694 is divided by 93

The number which is getting divided here is called the dividend.

69694 is dividend

The number which divides a given number is the divisor.

93 is the divisor.

the number which we get as a result is known as the quotient.

The divisor which does not divide a number completely produces a number, which is referred to as remainder.

69694 can be written as (69657+37)

69657 is divisible completely by 93 and the remainder is 37.

Hence, 37 is the remainder when 69,694 is divided by 93

To learn more on Division click:

https://brainly.com/question/21416852

#SPJ2

Simplifying Expressions ,

Answers

17? Let me know if it’s right

1. You decide to buy some new clothes. The subtotal comes to $123.79, but
you have a 15% off coupon. What is the total you will spend? *

Answers

Answer:

$105.22

Step-by-step explanation:

XY−→− bisects ∠WXZ and m∠WXY=29∘. Find m∠ZXY and m∠ZXW.

Answers

Answer:

29° and 58°

Step-by-step explanation:

Since XY bisects ∠ WXZ then ∠ WXY and ∠ ZXY are congruent, thus

∠ ZXY = ∠ WXY = 29°

∠ ZXW = ∠ WXY + ∠ ZXY = 29° + 29° = 58°

Which ordered pair is in the solution y>=1/3x+4

A. (-6,1)
B. (1,-6)
C. (6,-1)
D. (-1,6)

Answers

A the answer I think
I think it would be A
Other Questions
Which series of transformations would result in a figure that is congruent to the triangle ABC?rotation of 180' clockwise about the origin and then dilation with a scale factor of -1, centered at the originrotation of 180' clockwise about the origin and then dilation with a scale factor of 2, centered at the originreflection across the line y ox and then dilation with a scale factor of -3, centered at the origintranslation 3 units to right and then dilation with a scale factor of 3, centered at the origin I need help with this worksheet I don't understand from 12-14 Rank the following maps and geospatial technologies in terms of their privacy concerns, listing them fromgreatest privacy concern to least privacy concernA. geotagging, volunteered geographic information, mashup, citizen science, Mercator B. Mashup, geotagging, citizen science, volunteered geographic information, Mercator projection C. Mercator projection, Robinson projection, GPS, GIS, geotagging D. Robinson projection, geotagging, GPS, GIS, Goode Homolosine projectionE. GPS, GIS, volunteered geographic information, mental maps, geotagging Pls help its due todayyy An airplane is flying overhead at a constant elevation of 4090 ft. A person is viewing the plane from a position 3010 ft from the base of a radio tower. The airplane is flying horizontally away from the person. If the plane is flying at the rate of 700 ft/s, at what rate is the distance between the person and the plane increasing when the plane passes over the radio tower The recipe makes enough stew for 6 people, and the ingredients cost $9.75. How much would it cost to serve 24 people? A student solved the problem using the proportion StartFraction 6 over 9.75 EndFraction = StartFraction c over 24 EndFraction Explain the error in this proportion. FOR THOSE WHO WANT A CHALLENGE owen has a collection of quarters nad nickels worth 8.10. if the nickels were quarters and the quarters were nickels, the value would be 17.70. find the number of each coin. Please help!! Will Mark brainliest!! If 12 roses cost 30.4 how much will 18 roses cost? Find the equation of a line that passes through the points (1,-3) and (3,-7).Leave your answer in the form y=mx + c Help me please thank you Which of the following reveals an event in the rising action? A. In the brightness of the wintry sun next morning as it streamed over the breakfast table he laughed at his fears. B. "Herbert will have some more of his funny remarks, I expect, when he comes home," she said, as they sat at dinner. C. His mother laughed, and following him to the door, watched him down the road; and returning to the breakfast table, was very happy at the expense of her husband's credulity. D. His wife made no reply. She was watching the mysterious movements of a man outside, who, peering in an undecided fashion at the house, appeared to be trying to make up his mind to enter. Do trees keep their internal parts separate from the outside environment? does breast cancer occur in men? what are the signs and symptoms?actually anatomy & physiology Which 2 subjects are 2 unit apart The raft back and forth on the ragged sea as the frigid waters at its weathered hull. Identify number 8and number 11 After all markdowns and discounts, Charlene's prom dress cost her $22 before tax. The dress was on a rack labeled "50% off lowest marked price," and the lowest marked price was already a 75% reduction from the original price. What was the original price of the dress? I promise u your gonna have a bright future if u help me with this ! and I'll brainlist A graphic artist works for a large public relations firm. He hopes to work his way up to the position of art director. How much will he make if he gets this position?