Question

Fatorando a expressão 64 – 9a4b2 obtemos: *
a) (8 + 3ab)(8 – 3ab)
b) (8 + 3ab2)(8 – 3ab2)
c) (8 + 3a2b2)(8 – 3a2b2)
d) (8 + 3a2b)(8 – 3a2b)

Answer 1

$\boxed{\begin{array}{l}\underline{\rm Fatorac_{\!\!,}\tilde ao~da~diferenc_{\!\!,} a~de~dois~quadrados}\\\boxed{\boxed{\boxed{\boxed{\sf a^2-b^2=(a+b)(a-b)}}}}\\\sf 64-9a^4b^2\\\sf a^2=64~~a=\sqrt{64}~~a=8\\\sf b^2=9a^4b^2~~b=\sqrt{9a^4b^2}~~b=3a^2b\\\sf 64-9a^4b^2=(8+3a^2b)(8-3a^2b)\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~d}}}}\end{array}}$