Expand the expression (2x – 3)6
Question:

Expand the expression $(2 x-3)^{6}$

Solution:

By using Binomial Theorem, the expression $(2 x-3)^{6}$ can be expanded as

$(2 x-3)^{6}={ }^{6} \mathrm{C}_{0}(2 x)^{6}-{ }^{6} \mathrm{C}_{1}(2 x)^{5}(3)+{ }^{6} \mathrm{C}_{2}(2 x)^{4}(3)^{2}-{ }^{6} \mathrm{C}_{3}(2 x)^{3}(3)^{3}$

$\begin{aligned} &+{ }^{6} \mathrm{C}_{+}(2 x)^{2}(3)^{4}-{ }^{6} \mathrm{C}_{5}(2 x)(3)^{5}+{ }^{6} \mathrm{C}_{6}(3)^{6} \\=& 64 x^{6}-6\left(32 x^{5}\right)(3)+15\left(16 x^{4}\right)(9)-20\left(8 x^{3}\right)(27) \\ &+15\left(4 x^{2}\right)(81)-6(2 x)(243)+729 \end{aligned}$

$=64 x^{6}-576 x^{5}+2160 x^{4}-4320 x^{3}+4860 x^{2}-2916 x+729$

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