Question

Verify the following:

$\left(v\right)(a+b)(a+b)(a+b)=(a^3+3a^{2}b+3a{b}^2+b^3)$

Answer 1

$L.H.S.$

$=(a+b)(a+b)(a+b)$

$=(a+b)(a+b{)}^2$

$=(a+b)(a^2+2ab+b^2)$

$=a(a^2+2ab+b^2)+b(a^2+2ab+b^2)$

$=a^3+2a^{2}b+b^{2}a+a^{2}b+2b^{2}a+b^3$

$=a^3+3a^{2}b+3a{b}^2+b^3$

$=R.H.S.$

Hence, verified.