Question

How to expand (x^2-3y)^6​

Answer 1

$\red{ Expansion \: of \: ( x^{2} - 3y )^{6} }$

$= ^{6}C_{0} (x^{2})^{6} - ^{6}C_{1} (x^{2})^{5}(3y)$

$+ ^{6}C_{2} (x^{2})^{4}(3y)^{2}-^{6}C_{3} (x^{2})^{3}(3y)^{3}$

$+ ^{6}C_{4} (x^{2})^{2}(3y)^{4}-^{6}C_{5} (x^{2})(3y)^{5}$

$+ ^{6}C_{6} (3y)^{6}$

$= 1 \times x^{12} - 6\times x^{10}\times 3y + 15 \times x^{8} \times 9y^{2}$

$- 20 \times x^{6} \times 27y^{3} + 15 \times x^{4} \times 81y^{4}$

$- 6 x^{2} \times 243y^{5} + 729y^{6}$

$= x^{12} -18x^{10}y + 135x^{8}y^{2} - 540x^{6}y^{3}$

$+ 1215x^{4}y^{4} - 1458x^{2}y^{5} + 729y^{6}$

Therefore.,

$\red{ Expansion \: of \: ( x^{2} - 3y )^{6} }$

$\green { = x^{12} -18x^{10}y + 135x^{8}y^{2} - 540x^{6}y^{3}}$

$\green { + 1215x^{4}y^{4} - 1458x^{2}y^{5} + 729y^{6}}$

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