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# Find the expansion of $(3x^2-2ax+3a^2)^3$ using Binomial theorem

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Toolbox:
• $(a-b)^n=nC_0a^n-nC_1a^{n-1}b+nC_2a^{n-2}b^2-....+(-1)^nnC_ra^{n-r}b^r+.....+nC_n(-b)^n$
$[3x^2-a(2x-3a)]^3=(3x^2)^3-3C_1(3x^2)^2.a(2x-3a)+3C_2(3x^2)a^2(2x-3a)^2-a^3(2x-3a)^3$
$\Rightarrow 27x^6-27x^4a(2x-3a)+9x^2a^2(4x^2-12ax+9a^2)-a^3(8x^3-3\times 4\times x^2\times 3a+3\times 2x\times 9a^2-27a^3)$
$\Rightarrow 27x^6-54x^5a+81a^2x^4-108a^3x^3+81a^4x^2-8a^3x^3+36a^4x^2-54a^5x+27a^6$
$\Rightarrow 27x^6-54x^5a+117a^2x^4-116a^3x^3+117a^4x^2-54a^5x+27a^6$
answered Jun 24, 2014