The Math Blog: Factor `x^4

This expression can be factored as a difference of two squares because 81 is a square number. Rewrite 81 as

$x^4$ as

$(x^2)^2$ ,

$9^2 = (3^2)^2$ and

$y^4$ as

$(y^2)^2$ ,

$(x^2)^2 - (3^2)^2 * (y^2)^2$

Combine

$(3^2)^2$ and

$(y^2)^2$ ,

$(x^2)^2 - ((3y)^2)^2$

Applying the difference of squares formula,

$(x^2 + (3y)^2)(x^2 - (3y)^2)$

Applying the difference of squares formula on the second parenthesis,

$(x^2 + (3y)^2)(x + 3y)(x - 3y)$

Simplify by rewriting (3y)^2 as 9y^2,

$(x^2 + 9y^2)(x + 3y)(x - 3y)$

Thus the expression

$x^4 - 81y^4$ is completely factored to

$(x^2 + 9y^2)(x + 3y)(x - 3y)$

The Math Blog