Expand the given expression (2x - 3)6 - Vidyadip

Question

Expand the given expression (2x - 3)⁶

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Answer

Using binomial theorem for the expansion of (2x - 3)⁶ we have
${(2x - 3)^6}{ = ^6}{C_0}{(2x)^6}{ + ^6}{C_1}{(2x)^5}( - 3)$${ + ^6}{C_2}{(2x)^4}{( - 3)^2}{ + ^6}{C_3}{(2x)^3}{( - 3)^3}$
${ + ^6}{C_4}{(2x)^2}{( - 3)^4}{ + ^6}{C_5}2{x^5}{( - 3)^2}$${ + ^6}{C_6}{( - 3)^6}$
= 64x⁶ + 6.32x⁵ (-3) + 15.16x⁴.9 + 20.8x³ (-27) + 15.4x².81 + 6.2x (-243) + 729
= 64x⁶ - 576x⁵ + 2160x⁴ - 4320x³ + 4860x² - 2916x + 729

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