Homework Answers
According to Binomial theorem,
(a + b)n = nC0 an b0 + nC1 an-1 b1 + nC2 an-2 b2 + ...... nCn a0 bn
Substituting a = 1 and b = 1 in the above theorem
=> (1 + 1)n = nC0 1n 10 + nC1 1n-1 11 + nC2 1n-2 12 + ...... nCn 10 1n
=> 2n = nC0 * 1 + nC1 * 1 + nC2 * 1 + ...... nCn * 1
=> 2n = nC0 + nC1 + nC2 + ...... nCn
=> 
=
2n.
(b) (a2 + b)4
= 4C0 (a2)4 b0 + 4C1 (a2)3 b1 + 4C2 (a2)2 b2 + 4C3 (a2)1 b3 + 4C4 (a2)0 b4
= 1 * a8 * 1 + 4 * a6 * b + 6 * a4 * b2 + 4 * a2 * b3 + 1 * 1 * b4
= a8 + 4a6b + 6a4b2 + 4a2b3 + b4.
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