## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$81t^4-72t^2+16$
RECALL: $x^my^m=(xy)^m$ Use the rule above to obtain: $=[(3t+2)(3t-2)]^2$ Multiply the two binomials using the formula $(a+b)(a-b)=a^2-b^2$ to obtain: $=[(3t)^2-2^2]^2 \\=(9t^2-4)^2$ Use the formula $(a-b)^2=a^2-2ab+b^2$ with $a=9t^2$ and $b=4$ to obtain: $=(9t^2)^2-2(9t^2)(4)+4^2 \\=81t^4-72t^2+16$