Question
Expand the given expression $(1 - 2x)^5$
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Answer
Using binomial theorem for the expansion of $(1 - 2x)^5 $ we have
${(1 - 2x)^5}{ = ^5}{C_0}{ + ^5}{C_1}( - 2x)+\ ^5{C_2}{( - 2x)^2}{ + ^5}{C_3}{( - 2x)^3}{ + ^5}{C_4}{( - 2x)^4}$${ + ^5}{C_5}{( - 2x)^5}$
$= 1 + 5 (-2x) + 10(-2x)^2 + 10(-2x)^3 + 5(-2x)^4 + (-2x)^5$
$= 1 - 10x + 40x^2 - 80x^3 + 80x^4 - 32x^5$
${(1 - 2x)^5}{ = ^5}{C_0}{ + ^5}{C_1}( - 2x)+\ ^5{C_2}{( - 2x)^2}{ + ^5}{C_3}{( - 2x)^3}{ + ^5}{C_4}{( - 2x)^4}$${ + ^5}{C_5}{( - 2x)^5}$
$= 1 + 5 (-2x) + 10(-2x)^2 + 10(-2x)^3 + 5(-2x)^4 + (-2x)^5$
$= 1 - 10x + 40x^2 - 80x^3 + 80x^4 - 32x^5$
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