Question

Factorize the following:
$20a^{12}{b}^2-15a^8{b}^4$

Answer 1

The greatest common factor of the terms $20a^{12}{b}^2$ and $-15a^8{b}^4$ of the expressions is $5a^8{b}^2.$
$20a^{12}{b}^2=5\times 4\times a^8\times a^4\times b^2=5a^8{b}^2\times 4a^4$

and, $-15a^8{b}^4=5\times -3\times a^8\times b^2\times b^2=5a^8{b}^2\times (-3b^2)$

$20a^{12}{b}^2-15a^8{b}^4=5a^8{b}^2\times 4a^4-5a^8{b}^2\times \left(3b^2\right)$

$=5a^8{b}^2(4a^4-3b^2)$

Hence, the expression $20a^{12}{b}^2-15a^8{b}^4$ can be factorised as $5a^8{b}^2(4a^4-3b^2)$​​