Expand the given expression (1 - 2x)5 - Vidyadip

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 + 40x² - 80x³ + 80x⁴ - 32x⁵

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