Question

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

Answer 1

$20a^{12}{b}^2-15a^8{b}^4$

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

$=5a^8{b}^2({\left(\sqrt{2}a\right)}^4-{\left(\sqrt{3}b\right)}^2)$

$=5a^8{b}^2({\left(\sqrt{2}a\right)}^2+{\left(\sqrt{3}b\right)}^2)({\left(\sqrt{2}a\right)}^2-{\left(\sqrt{3}b\right)}^2)$

$=5a^8{b}^2({\left(\sqrt{2}a\right)}^2+{\left(\sqrt{3}b\right)}^2)(\sqrt{2}a-\sqrt{3}b)(\sqrt{2}a+\sqrt{3}b)$