## College Algebra (11th Edition)

$(x^2+4)(x+2)(x-2)$
$\bf{\text{Solution Outline:}}$ To factor the given expression, $x^4-16 ,$ use the factoring of the difference of $2$ squares. $\bf{\text{Solution Details:}}$ The expressions $x^4$ and $16$ are both perfect squares and are separated by a minus sign. Hence, $x^4-16 ,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to \begin{array}{l}\require{cancel} (x^2+4)(x^2-4) .\end{array} The expressions $x^2$ and $4$ are both perfect squares and are separated by a minus sign. Hence, $x^2-4 ,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to \begin{array}{l}\require{cancel} (x^2+4)(x+2)(x-2) .\end{array}