Verify the following: (a - b)(a - b)(a - b) = a^3- 3a^2b + 3ab^2-… - Vidyadip

Question

Verify the following:$ (a - b)(a - b)(a - b) = a^3- 3a^2b + 3ab^2- b^3$

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Answer

$ (a - b)(a - b)(a - b) = a^3- 3a^2b + 3ab^2- b^3$
Taking $LHS$
$ =(a-b)(a-b)(a-b) $
$ =(a-b)(a-b)^2 $
$ =(a-b)\left(a^2-b^2+2 a b\right) $
$ =a\left(a^2-2 a b+b^2\right)-b\left(a^2-2 a b+b^2\right) $
$=a^3-2 a^2 b+a b^2-b a^2+2 a b^2-b^3 $
$ =a^3-3 a^2 b+3 a b^2-b $
$= RHS$
Hence verified

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