Question

A student factors a6 - 64 to (a2 - 4)(a4 4a2 16).

Answer 1

Answer:

Option (b) is correct.

The expression is equivalent, but the $a^2-4$  term is not completely factored.

Step-by-step explanation:

Given :  a student factors $a^6-64$ to $(a^2-4)(a^4+4a^2+16).$

We have to choose the correct statement  about  $(a^2-4)(a^4+4a^2+16).$ from the given options.

Given  $a^6-64$ is factored to $(a^2-4)(a^4+4a^2+16).$

Consider  $a^6-64$  

Using algebraic identity, $a^3-b^3=(a-b)(a^2+ab+b^2)$

comparing $a=a^2$ and b = 4, we have,

$(a^2)^3-4^3=(a^2-4)(a^4+4a^2+16)$

Thus, the factorization is equivalent but we can simplify it further also, as

Using algebraic identity, $a^2-b^2=(a+b)(a-b)$

Thus, $a^2-4=a^2-2^2$

Can be written as $a^2-4=(a+2)(a-2)$

Thus, the expression is equivalent, but the $a^2-4$  term is not completely factored.

Option (b) is correct.

Answer 2

B is correct on edge