Question

Разложить на множители
$64a^{4}+81$

Answer 1

$64a^{4}+81=(2sqrt{2}a)^{4} +3^{4} =(2sqrt{2}a)^{4}+3^{4}+2*(2sqrt{2}a)^{2}*3^{2}-2*(2sqrt{2}a)^{2}*3^{2}=((2sqrt{2}a)^{2}+3^{2})^{2}-2*(2sqrt{2}a)^{2}*3^{2}=(8a^{2}+9)^{2} -144a^{2}=(8a^{2}-12a+9)(8a^{2} +12a+9)$