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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Updated on: 10-Oct-2022

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