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Expand the expression (1– 2x)5

Question:

Expand the expression $(1-2 x)^{5}$

Solution:

By using Binomial Theorem, the expression $(1-2 x)^{5}$ can be expanded as

$(1-2 x)^{5}$

$={ }^{5} C_{0}(1)^{5}-{ }^{5} C_{1}(1)^{4}(2 x)+{ }^{3} C_{2}(1)^{3}(2 x)^{2}-{ }^{5} C_{3}(1)^{2}(2 x)^{3}+{ }^{5} C_{4}(1)^{1}(2 x)^{4}-{ }^{5} C_{5}(2 x)^{5}$

$=1-5(2 x)+10\left(4 x^{2}\right)-10\left(8 x^{3}\right)+5\left(16 x^{4}\right)-\left(32 x^{5}\right)$

$=1-10 x+40 x^{2}-80 x^{3}+80 x^{4}-32 x^{5}$

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