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

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Find the expansion

(3 x^{2} - 2 a x + 3 a^{2})^{3}

using binomial theorem.

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Text solutionVerified

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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Question Text	Find the expansion $(3 x^{2} - 2 a x + 3 a^{2})^{3}$ using binomial theorem.
Answer Type	Text solution:1
Upvotes	150