Question

How do you factor the trinomial `a^4 - 8a^2 + 16`?

Answer 1

`a^4-8a^2+16=color(green)((a-2)^2(a+2)^2)`

Explanation:

Temporarily replace `a^2` with b#

The expression becomes
`color(white)("XXX")b^2-8b+16`
which factors easily as
`color(white)("XXX")(b-4)^2`

But `(b-4) = (a^2-4)`
which can be factored as `(a+2)(a-2)`

So
`color(white)("XXX")a^4-8a^2+16=(b-4)^2`
`color(white)("XXXXXXXXXXX")= ((a+2)(a-2))^2`
`color(white)("XXXXXXXXXXX") = (a+2)^2(a-2)^2`