Question

A student factors a6 - 64 to (a2 - 4)(a4 + 4a2 + 16).Which statement about (a2 − 4)(a4 + 4a2 + 16) is correct?

Answer 1

Answer:

Option (b) is correct.

The expression is equivalent, but the   term is not completely factored.

Step-by-step explanation:

Given :  a student factors  to

We have to choose the correct statement  about   from the given options.

Given   is factored to

Consider    

Using algebraic identity,

comparing  and b = 4, we have,

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

Using algebraic identity,

Thus,

Can be written as

Thus, the expression is equivalent, but the   term is not completely factored.

Option (b) is correct.