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LenaWriter [7]
3 years ago
14

which product will result in a sum or difference of cubes? (x 7)(x2 – 7x 14) (x 8)(x2 8x 64) (x – 9)(x2 9x 81) (x – 10)(x2 – 10x

100)
Mathematics
2 answers:
Alina [70]3 years ago
6 0
Hello,
++++++++++++++++++++++++
Answer C
++++++++++++++++++++++++

x^3+7^3=(x+7)(x²-7x+49) A: False (+14)
x^3+8^3=(x+8)(x²-8x+64) B:False  (+8x)
x^3-10^3=(x-10)(x²+10x+100) D:False (-10x)


poizon [28]3 years ago
5 0

Answer:

option (3) satisfies the  products that  will result in a difference of cubes.

(x-9)(x^2+9x+81)=x^3-3^3

Step-by-step explanation:

Given : Some options.

We have to choose the  products that  will result in a sum or difference of cubes.

A sum or difference of cubes is given by:

a^3-b^3=(a-b)(a^2+b^2+ab)

and a^3+b^3=(a+b)(a^2+b^2-ab)

Thus, out of given

(x-9)(x^2+9x+81) is in the same form as a^3-b^3 where a = x and b = 9.

Thus, (x-9)(x^2+9x+81)=x^3-3^3=x^3-729

Thus, only option (3) satisfies the  products that  will result in a difference of cubes.

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