Question

Factor 64 – x15. (4 – x3)(16 + 4x3 + x3) (4 – x3)(16 + 4x3 + x6) (4 – x5)(16 + 4x5 + x5) (4 – x5)(16 + 4x5 + x10)

Answer 1

(4-x^5) (16+4x^5+x^10)
I hope this helps!

Answer 2

Option d)
`(4-x^5)(16+x^(10)+4x^5)`

Explanation:

We are given the following in the question.

`64-x^(15)`

We have to factorize the given expression.

Using the algebraic identity:

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

`64-x^(15)\\\\(4)^3 - (x^5)^3\\\\(4 - x^5)(4^2 + (x^5)^2 + 4x^5)\\\\(4-x^5)(16+x^(10)+4x^5)`

Hence, the factors of given expression is given by option d)
`(4-x^5)(16+x^(10)+4x^5)`