Question

How do you factor the expression `a^4 - 81`?

Answer 1

`a^4-81=(a^2+9)(a+3)(a-3)`

Explanation:

`(a^4-81)=((a^2)^2-9^2)`
and is therefore the difference of squares with factors
`color(white)("XXX")(a^2+9)(a^2-9)`

but `(a^2-9) = (a^2-3^2)`
is also the difference of squares with factors
`color(white)("XXX")(a+3)(a-3)`

`"---------------------------------------------------------------------"`

Remember: Factoring the Difference of Squares
`color(white)("XXX")(x^2-y^2) = (x+y)(x-y)`