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

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Text solutionVerified

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) +^{5} 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 (4 x^{2}) - 10 (8 x^{3}) + 5 (16 x^{4}) - (32 x^{5})

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

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