Question

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)

Answer 1

Hello,
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Answer C
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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)

Answer 2

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

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

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.