(1+a)6 = 6C0 (1)6 (a)0 + 6C1 (1)5 (a)1 + 6C2 (1)4 (a)2 + 6C3 (1)3 (a)3 + 6C4 (1)2 (a)4 + 6C5 (1)1 (a)5 + 6C5 (1)0 (a)6
= 1 × 1 × 1 + 6 × 1 × a + 15 × 1 × a2 + 20 × 1 × a3+ 15 × 1 × a4 + 6 × 1 × a5 + 1 × 1 × a6
= 1 + 6a + 15a2 + 20a3 + 15a4 + 6a5 + a6
a = 2 रखने पर
LHS = (1 + a)6 = (1 + 2)6 = (3)6 = 729
RHS = 1 + 6a + 15a2 + 20a3 + 15a4 + 6a5 + a6
= 1 + 6 × 2 + 15 × (2)2 + 20 (2)3 + 15 (2)4 + 6 (2)5 + (2)6
= 1 + 12 + 60 + 20 × 8 + 15 × 16 + 6 × 32 + 64
= 1 + 12 + 60 + 160 + 240 + 192 + 64
= 729
इसलिए LHS = RHS
