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Pascal Triangle

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Question

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

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Solution

Using binomial theorem for the expansion of $(2 x - 3)^{6}$ , we have

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

$= 64 x^{6} + 6.32 x^{5} (- 3) + 15.16 x^{4} .9 + 20.8 x^{3} (- 27) + 15.4 x^{2} .81 + 6.2 x (- 243) + 729$

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

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