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Expand (1 + x)5 and verify by putting x = 1 on both sides.

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(1 + x)5

5C0 . 1 . x0 + 5C1 . 1 . x1 + 5C2 1 x2 + 5C3 . 1 . x3 + 5C4 1 x4 + 5C5 . 1 . x5

= 1+ 5x + 10x2 + 10x3 + 5x4 + x5

LHS = (1 + x)5

Putting x = 1,

LHS = (1 + 1)5 = (2)5 = 32

RHS = 1 + 5x + 10x2 + 10x3 + 5x4 + 1

Putting x = 1.

RHS= 1 +5(1)+ 10(1)2+ 10(1)3 + 5(1)4 + 15

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

Hence, LHS = RHS

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