Question

What is the completely factored form of this polynomial?
81x4 - 16/A
A. (3x2 + 2y?)(9x+47)(9x - 4y)
B. (9x2 + 4y?)(9x2 - 4y?)
C. (9x2 + 4y713x – 2y12
D. (9x + 4y)(3x+27)(3x – 2y)

Answer 1

$81x^4-16y^4\implies 3^4x^4-2^4y^4\implies (3x)^4-(2y)^4\implies \underset{\textit{difference of squares}}{[(3x)^2]^2-[(2y)^2]^2} \\\\\\ \underset{\textit{difference of squares}}{[(3x)^2-(2y)^2]}[(3x)^2+(2y)^2]\implies (3x-2y)(3x+2y)[(3x)^2+(2y)^2] \\\\\\ (3x-2y)(3x+2y)[(3^2x^2)+(2^2y^2)]\implies (3x-2y)(3x+2y)(9x^2+4y^2)$