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Binomial Expression

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Question

Expand the following binomial:
${(1 - 3 a^{2})}^{6}$

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Solution

using binomial theorem
${(x + y)}^{n}$

$\Rightarrow n \sum r = 0_{r}^{n} C x^{n - r} y^{r}$

${(1 - 3 a^{2})}^{6}$

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

$= 1 - 18 a^{2} + 135 a^{4} - 540 a^{6} + 1215 a^{8} - 1458 a^{10} + 729 a^{12}$

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