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Rational Expression

Simplify: 3x...

Question

Simplify:
$((3 x^{2} - 2 a x) + 3 a^{2})^{3}$

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Solution

${((3 x^{2} - 2 a x) + 3 a^{2})}^{3}$
$= {(3 x^{2} - 2 a x)}^{3} + {(3 a^{2})}^{3} + 3 \times 3 a^{2} (3 x^{2} - 2 a x) ((3 x^{2} - 2 a x) + 3 a^{2})$
$= 27 x^{6} - 8 a^{3} x^{3} - 3 \times 3 x^{2} \times 2 a x (3 x^{2} - 2 a x) + 27 a^{6} + 9 a^{2} (3 x^{2} - 2 a x) (3 x^{2} - 2 a x + 3 a^{2})$
$= 27 x^{6} - 8 a^{3} x^{3} - 18 a x^{3} (3 x^{2} - 2 a x) + 27 a^{6} + 9 a^{2} (9 x^{4} - 6 a x^{3} + 9 x^{2} a^{2} - 6 a x^{3} + 4 a^{2} x^{2} - 6 a^{3} x)$
$= 27 x^{6} - 8 a^{3} x^{3} - 54 a x^{5} + 36 a^{2} x^{4} + 27 a^{6} + 81 a^{2} x^{4} - 54 a^{3} x^{3} + 81 a^{4} x^{2} - 54 a^{3} x^{3} + 36 a^{4} x^{2} - 54 a^{5} x$
$= 27 x^{6} - 54 a x^{5} + 117 a^{2} x^{4} - 116 a^{3} x^{3} + 117 a^{4} x^{2} - 54 a^{5} x + 27 a^{6}$

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Similar questions

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

Q. Find the expansion of

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

Q. Find the expansion

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

using binomial theorem.

\frac{3 x^{2}}{3 x^{2}}

(a^{2} - b^{2}) x^{2} + 2 a x + 1

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