Question

Solve:
$51a^6(256a^4-81b^4)÷34(4a-3b)$

Answer 1

$51a^6(256a^4-81b^4)÷34(4a-3b)$

$51a^6\left[\right(4a{)}^4-\left(3b{)}^4\right]\times \frac{1}{34(4a-3b)}$

$=\frac{51a^6\left[\right(4a{)}^2-\left(3b{)}^2\right]\left[\right(4a{)}^2+\left(3b{)}^2\right]}{34(4a-3b)}$

$=\frac{3a^6\left[\right(4a-3b\left)\right(4a+3b\left)\right][16a^2+a{b}^2]}{2(4a-3b)}$

$=\frac{3}{2}{a}^6(4a+3b)(16a^2+a{b}^2)$

Hence, this is the answer.