Using binomial theorem, expand each of the following:

(1 – 2x)5


To find: Expansion of (1 – 2x)5


Formula used: (i)


(ii) (a+b)n = nC0an + nC1an-1b + nC2an-2b2 + …… +nCn-1abn-1 + nCnbn


We have, (1 – 2x)5


[5C0(1)5] + [5C1(1)5-1(-2x)1] + [5C2(1)5-2(-2x)2] + [5C3(1)5-3(-2x)3]+ [5C4(1)5-4(-2x)4] + [5C5(-2x)5]




1 – 5(2x) + 10(4x2) – 10(8x3) + 5(16x4) – 1(32x5)


1 – 10x + 40x2 – 80x3 + 80x4 – 32x5


On rearranging


Ans) –32x5 + 80x4 – 80x3 + 40x2 – 10x + 1


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