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

CAN SOMEONE HELP ME PLEASE ?!

Answers

Answer:

A. XY

Step-by-step explanation:

The answer is XY because it is the same length as XZ. I didn't determine this by guessing, but by eliminating the wrong answer choices. The tick marks indicate what lines are congruent to each other. The answer can't be C because AY is congruent to YC since they both have 3 tick marks, indicating that they are congruent to each other. Same goes for the others.

Larry is putting a row of rocks around his rectangular pool. Which descriptive model will tell him how many rocks he needs?

[2(pool length) + 2(pool width)] times the width of the rocks

(pool length times pool width) times the width of the rocks

(pool length times pool width) divided by the width of the rocks

[2(pool length) + 2(pool width)] divided by the width of the rocks

Answers

Answer:

P = [2( l)+2(w)] / width of the rock

Step-by-step explanation:

row of rocks around his rectangular pool, this tells us we are finding the perimeter

The perimeter of a rectangle is given by

P = 2( l+w)

P = 2( l)+2(w)

But we know that the length  takes into account the width of the rock so divide each side by the width of the rock

P = [2( l)+2(w)] / width of the rock

The given measurement of a surface Area of a sphere is 196π.Find it's radius
(thanks in advance)​

Answers

Answer:

Hope this solution helps you. Sorry for the handwriting .

can anyone pls helppppp

Answers

hourly rate:
39(1.3r) = 541.80
(hours times hourly rate equals profit)

then solve
1.3r = 13.89
r = 10.69

the hourly rate is $10.69


to answer the bottom question, 390 + 117 = 507, but that’s not close to 541.80 so I have no idea what they’re asking there

What is 4 divided by 3/5

Answers

Answer:

20/3 or 6 2/3

Step-by-step explanation: 4/1 times 5/3           multiply and you get 20/3

Answer:

6 2/3

Step-by-step explanation:

The total cost after tax to repair Deborah's computer is represented by 0.09(60h)+60h, where h represents the number of hours it takes to repair Deborah's computer. What part of the expression represents the amount of tax Deborah has to pay? Explain.

Answers

Answer:

0.09(60h)

Step-by-step explanation:

The part that represents the tax is 0.09.

This is because, we can rewrite the sum as;

Amount of tax + Total cost for the number of hours

Now, the amount of tax can only be a percentage of the total

We can write 0.09 as 9/100

This can be interpreted as 9% of the total amount

So therefore we can rewrite the amount as;

9% of 60h + 60h

So the part that represents the amount of tax Deborah has to pay is 0.09(60h)

What is the slope of a line that is perpendicular to the line shown on the graph?

Answers

The slope of the line that is perpendicular to the line shown should have an opposite slope. For example if the slope is 2/5. The perpendicular slope is -5/2. Hope this helps!!

*EXTRA PTS PLS ANSWER* Find the equation of a line that has a slope of 1/2 and a y-intercept = 1. (Don't leave any spaces in between characters) *

Answers

Answer:

y = [tex]\frac{1}{2}[/tex] x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{1}{2}[/tex] and c = 1 , thus

y = [tex]\frac{1}{2}[/tex] x + 1 ← equation of line

Someone please help only answer if your 100 percent sure

Answers

Answer:

90

Step-by-step explanation:

Which two ratios form a proportion?
3:4 and 6:12
3:4 and 9:15
3:4 and 12:18
3:4 and 15:20

Answers

Answer:

3:4 and 15:20

Step-by-step explanation:

The answer is the fourth one because 3:4 and 15:20 are equivalent, so there's your answer. Hope it helps!

there are 48 newborn girls in a hospital nursery. For every 3 girls, there are 2 boys. How many newborn babies are in the nursery?

Answers

Hi! I believe your answer is 80 newborn babies. To find the number of boys, divide 48 by 3 (since it is for every 3 girls) and you'll get 16. Next, multiply 16 and 2 (for every 2 boys) and you'll get 32. Lastly, add 48 and 32 and you'll get the number of newborn babies in the nursery (80). I hope this helps you! Good luck and have a great day. ❤️✨

Number of total newborn babies = 80

What is ratio?

A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one.

Given,

Total number of girls = 48

For every 3 girls, there are 2 boys.

Ratio of girls to boy = 3/2

Let there are x boys,

then,

48/x = 3/2

3x = 96

x = 32

Number of boys = 32

Total newborn babies = Number of girls + number of boys

                                     = 48 + 32 = 80

Hence, 80 newborn babies are in nursery.

Learn more about ratio here:

https://brainly.com/question/1504221

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A student solved the equation below using the steps shown, rounding to two decimal places if necessary.

which step contains the first mistake ?

A. step 2

B. step 1

C. step 3

D. step 4

Answers

Answer:

Step 1

Step-by-step explanation:

please help me? im desperate!

Answers

Answer:

The same sign

Step-by-step explanation:

20 POINTS!! HELP ME PLZZ I NEED HELP WITH THIS!!

Answers

Answer:

0.22222222

Step-by-step explanation:

Hope this helps!!!

Answer:

0.22222222

Step-by-step explanation:

you have to divide 2 by 9.

Kainoa collects trading cards. He has 1,032 baseball cards, 709 basketball cards, and 833 football cards. He wants to put all of them in albums. Each page in the albums holds 18 cards. How many pages will he need to hold all of his cards? He will need pages

Answers

Answer:

143 pages

Step-by-step explanation:

Kainoa has:

1,032 baseball cards, 709 basketball cards, and 833 football cards.

Totally number of cards =

(1032 + 709 + 833)cards = 2574 cards

We are told that:

Each page in the albums holds 18 cards

The pages he will need to hold all of his cards is calculated as:

2574 cards ÷ 18 cards = 143 pages.

Compare the ratio of miles driven to gallons of gas used for Car A and Car D. Write the ratios as fractions and use a common denominator of 8. The ratio of miles to gallons for Car A is /8. The ratio of miles to gallon for Car D is /8. The ratio for Car A is the ratio for Car D.

Answers

Answer:

The ratio of miles to gallons for Car A is  

✔ 224

/8.

The ratio of miles to gallon for Car D is  

✔ 184

/8.

The ratio for Car A is  

✔ greater than

the ratio for Car D.

Step-by-step explanation:

What is the correct equation to find the value of X?

Answers

Answer:

x = 12

Step-by-step explanation:

The 2 angles shown are corresponding angles and congruent, thus

8x - 17 = 5x + 19 ( subtract 5x from both sides )

3x - 17 = 19 ( add 17 to both sides )

3x = 36 ( divide both sides by 3 )

x = 12

The regular price of a baseball hat is $15.65. If Julio buys the baseball hat on sale for 20% off the regular price, how much change will he receive after paying with $20?

Answers

Begin by multiplying $15.65 by 0.20 to find what 20% of the regular price is. This gives you 3.13, which in this situation means $3.13.
To find the price with discount subtract 15.65-3.13. This gives you $12.52.
To find out the change, subtract 20-12.52. This gives you $7.48.
So, he will receive $7.48 in change.
Hope this helps!

A person invests 1000 dollars in a bank. The bank pays 6% interest compounded
monthly. To the nearest tenth of a year, how long must the person
leave the money
in the bank until it reaches 3300 dollars?

Answers

Answer:

t=19.94841\approx 19.9 \text{ years}

t=19.94841≈19.9 years

Step-by-step explanation:

Aanya wrote the four equations that are shown below.

A

6 x minus 8 = 4 (x minus 2) + 2 x
B

3 (x minus 1) + 2 x = 3 (x minus 1) + 2

C

7 x + 2 minus x = 6 (x + 2)
D

4 (x + 3) + x = 5 (x + 1) + 7

She examined them, without solving them, to determine which has exactly one solution. Which of Aanya’s equations has exactly one solution?
6 x minus 8 = 4 (x minus 2) + 2 x
3 (x minus 1) + 2 x = 3 (x minus 1) + 2
7 x + 2 minus x = 6 (x + 2)
4 (x + 3) + x = 5 (x + 1) + 7

Answers

Answer:      

B

Step-by-step explanation:

.' )

Answer:

The answer is B.

Step-by-step explanation:

I just took the test.

PLEASE HELPPP I DONT UNDERSTAND

Answers

Step-by-step explanation:

You need to do the distributive property to answer this question.

Everything in the outside of the parenthesis needs to be multiplied by each number inside the parenthesis.

Hope this helps you!

Answer:

(3 ^2  x 2x^ 4 y^2  )

Step-by-step explanation:

Find the distance between each pair of points.
M(-2,5) N(-2,-4)

Answers

Answer:

9

Step-by-step explanation:

Landon is going to use a computer at an internet cafe. The cafe has an initial charge of $10 to use a computer and an additional charge of $0.80 for every minute of use. Write an equation for C , C, in terms of t , t, representing the total cost of using a computer for t t minutes at the internet cafe.

Answers

Answer:0.80t+10

Step-by-step explanation:

Which function has exactly three distinct real zeros? A. h(x) = (x − 9)2(x − 4)2 B. h(x) = x(x + 7)2 C. h(x) = (x − 3)(x + 1)(x + 3)(x + 8) D. h(x) = (x − 2)2(x + 4)(x − 1)

Answers

Answer: D is the correct answer .

D. h(x)= (x-2)^2(x+4)(x-1)

Step-by-step explanation: For Plato users the correct answer is D .

The function which has three distinct zeroes is h(x) = (x − 2)²(x + 4)(x − 1), the correct option is D.

What is a Function?

A function is a law that relates a dependent and an independent variable.

The zeroes of the function are the point at which the function value becomes 0.

The function which have three distinct real zeroes is

h(x) = (x − 2)²(x + 4)(x − 1)

(x-2)² = 0

x = 2

(x+4) = 0

x = -4

x-1 = 0

x = 1

To know more about Function

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WHAT IS THE LAST SENTANCE FOR DESPASITO IN ENGLISH!!!!!!!!!!!!!!11

Answers

Ojhhha amhenamajaja a Jajajaja and

If AABC = ADEC,
ZB = 2x + 31 and ZE = 7x - 24
A
D
B
E
x = [?]

Answers

/_ b = /_ e

2x + 31 = 7x - 24

5x = 55

x = 11

Write an expression for the sentence: Kelly has $120 to spend at the fair and spent $15 on food and wants to play games that cost 4$ each


Smart people can answer

Answers

120 - 15 - (4x) that should get you the correct answer if you can solve that

From 9:00 p.m. to 6:00 a.m., the temperature dropped 1.6 degrees Fahrenheit per hour.



What was the total change in temperature, in degrees Fahrenheit, between 9:00 p.m. and 6:00 a.m.?

Answers

Answer: help plz

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

Simplify the following - (32)²​

Answers

Answer:

=-1024

Step-by-step explanation:

Hope this helps (:

please help me with this

Answers

The answer to this is

A-254

Why?
Because angles 8, 5, 4, and 1 are all equal. Because of this, if angle 8 is equal to 127° so are the other three.
the answer for this problem is A !!
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