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}$
$= 64x^6 + 6.32x^5 (-3) + 15.16x^4.9 + 20.8x^3 (-27) + 15.4x^2.81 + 6.2x (-243) + 729$
$= 64x^6 - 576x^5 + 2160x^4 - 4320x^3 + 4860x^2 - 2916x + 729$

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