**(1 + x)**^{5}

= ^{5}C_{0} . 1 . x^{0} + ^{5}C_{1} . 1 . x^{1} + ^{5}C_{2} 1 x^{2} + ^{5}C_{3} . 1 . x^{3} + ^{5}C_{4} 1 x^{4} + ^{5}C_{5} . 1 . x^{5}

= 1+ 5x + 10x^{2} + 10x^{3} + 5x^{4} + x^{5}

LHS = (1 + x)^{5}

Putting x = 1,

LHS = (1 + 1)^{5} = (2)^{5} = 32

RHS = 1 + 5x + 10x^{2} + 10x^{3} + 5x^{4} + 1

Putting x = 1.

RHS= 1 +5(1)+ 10(1)^{2}+ 10(1)^{3} + 5(1)^{4} + 1^{5}

= 1 + 5 + 10 + 10 + 5 + 1 = 32

Hence, LHS = RHS