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)#

#"---------------------------------------------------------------------"#

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

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