Question

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

which statement about (a2 − 4)(a4 4a2 16) is correct?

the expression is equivalent and is completely factored.


the expression is equivalent, but the (a2 – 4) term is not completely factored.


the expression is equivalent, but the (a4 4a2 16) term is not completely factored.


the expression is not equivalent.

Answer 1

b

Explanation:

b on edg lol i just want points

Answer 2

Option (b) is correct.

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

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.