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Algebraic Identities (a-b)³

Find the expa...

Question

Find the expansion $(3 x^{2} - 2 a x + 3 a^{2})^{3}$ using binomial theorem.

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Solution

For binomial expansion first let's do a small pairing inside the bracket
${[{3 x}^{2} - a (2 x - 3 a)]}^{3}$
Now let's expand this as be normally do for two digit expansion.

${[{3 x}^{2} - a (2 x - 3 a)]}^{3} = {{(3 x}^{2})}^{3} - 3 C_{1} {{(3 x}^{2})}^{2} . a (2 x - 3 a) + 3 C_{2} {{(3 x}^{2})} . a^{2} (2 x - 3 a)^{2} - a^{3} (2 x - 3 a)^{3}$
${27 x}^{6} - 54 x^{5} a + 81 a^{2} x^{4} - 108 a^{3} x^{3} + 81 a^{4} x^{3} - 8 a^{3} x^{3} + 36 a^{4} x^{2} - 54 a^{5} x + 27 a^{6}$
${27 x}^{6} - 54 x^{5} a + 117 a^{2} x^{4} - 116 a^{3} x^{3} + 117 a^{4} x^{3} - 54 a^{5} x + 27 a^{6}$

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