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Factorize $a^2 - 4b^2+ a^3 - 8b^3-(a-2b) ^2$.
Given: Polynomial: $a^2 - 4b^2+ a^3 - 8b^3-(a-2b) ^2$.
To do: To factorize: $a^2 - 4b^2+ a^3 - 8b^3-(a-2b) ^2$.
Solution:
$a^2 - 4b^2+ a^3 - 8b^3-(a-2b) ^2$
$=a^2 - 4b^2+ a^3 - 8b^3-a^2-4b^2+4ab$.
$=a^3-8b^2-8b^3+4ab$
$=a^3-(2b)^3+4ab-8b^2$
$=( a-2b)( a^2+2ab+4b^2)+4b( a-2b)$
$=( a-2b)( a^2+2ab+4b^2+4b)$
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