Question
Verify the following: $(a + b)(a + b)(a + b) = a^3+ 3a^2b + 3ab^2+ b^3$
✓
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^3 $
$= RHS$
Hence verified
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^3 $
$= RHS$
Hence verified
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