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Binomial Expression

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Question

Expand the following binomials expressions.
$(x - 3)^{5}$

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Solution

$(x - 3)^{5} =^{5} C_{0} x^{5} +^{5} C_{1} x^{4} (- 3)^{1} +^{5} C_{2} x^{3} (- 3)^{2} +^{5} C_{3} x^{2} (- 3)^{3} +^{5} C_{4} x (- 3)^{4} +^{5} C_{5} (- 3)^{5}$
$= x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 243$

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