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

Mathematics

2 answers:

Dimas [21]3 years ago

6 0

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

arlik [135]3 years ago

4 0

Answer:

Option d) $(4-x^5)(16+x^{10}+4x^5)$

Step-by-step 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) $(4-x^5)(16+x^{10}+4x^5)$

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