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

1 Answer
Alan P.
Dec 9, 2015

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)

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

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