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

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

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Answer 1 · 2016-10-23T07:22:11

$64 x^{3} - 192 x^{2} y + 192 x y^{2} - 64 y^{3}$ $64x^3-192x^2y+192xy^2-64y^3$

Explanation:

The cubic difference of a binomial is:
${(a - b)}^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b$ $color(red)((a-b)^3=a^3-3a^2b+3ab^2-b^$

${(4 x - 4 y)}^{3} = {(4 x)}^{3} - 3 {(4 x)}^{2} (4 y) + 3 (4 x) {(4 y)}^{2}_{(4 y)}^{3}$ $(4x-4y)^3=color(red)((4x)^3-3(4x)^2(4y)+3(4x)(4y)^2_(4y)^3)$
${(4 x - 4 y)}^{3} = 64 x^{3} - 3 (16 x^{2}) (4 y) + 3 (4 x) (16 y^{2}) - 64 y^{3}$ $(4x-4y)^3=64x^3-3(16x^2)(4y)+3(4x)(16y^2)-64y^3$
${(4 x - 4 y)}^{3} = 64 x^{3} - 192 x^{2} y + 192 x y^{2} - 64 y^{3}$ $(4x-4y)^3=64x^3-192x^2y+192xy^2-64y^3$

There is not like polynomials in the above expanded form
hint: $x^{2} y \neq x y^{2}$ $color(blue)(x^2y!=xy^2)$

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

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