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Question

Mathematics Question on Binomial Theorem for Positive Integral Indices

Expand the expression (1−2x)5(1- 2x)^ 5.

Answer

By using Bionomial Theorem, the expression (1−2x)5(1-2x)^5 can be expanded as
(1−2x)5(1-2x)^5
= 5C0(1)5−5C1(1)4(2x)+5C2(1)3(2x)2−5C3(1)2(2x)3+5C4(1)1(2x)4−5C5(2x)5 ^5C_0 (1)^5 - ^5C_1 (1)^4 (2x) + ^5C_2 (1)^3 (2x)^2 - ^5C_3 (1)^2 (2x)^3 + ^5C_4 (1)1 (2x)^4 - ^5C_5 (2x)^5
=1−5(2x)+10(4x2)−10(8x3)+5(16x4)−(32x5)1-5(2x)+10(4x^2)-10(8x^3)+5(16x^4)-(32x^5)
=1−10x+40x2−80x3+80x4−32x51-10x+40x^2-80x^3+80x^4-32x^5