How do you expand ${(x^{4} - y^{3})}^{3}$ $(x^4-y^3)^3$ ?

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How do you expand ${(x^{4} - y^{3})}^{3}$ $(x^4-y^3)^3$ ?

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Answer 1 · 2016-07-06T06:19:44

$x^{12} - 3 x^{8} y^{3} + 3 x^{4} y^{6} - y^{9}$ $x^12-3x^8y^3+3x^4y^6-y^9$

Explanation:

Since

${(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$ $(a+b)^3=a^3+3a^2b+3ab^2+b^3$

you have:

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

that's

$x^{12} - 3 x^{8} y^{3} + 3 x^{4} y^{6} - y^{9}$ $x^12-3x^8y^3+3x^4y^6-y^9$

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