How do you expand ${(2 x + 2 y)}^{4}$ $(2x+2y)^4$ ?

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How do you expand ${(2 x + 2 y)}^{4}$ $(2x+2y)^4$ ?

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Answer 1 · 2016-08-30T06:25:49

$16 x^{4} + 64 x^{3} y + 96 x^{2} y^{2} + 64 x y^{3} + 16 y^{4}$ $16x^4+64x^3y+96x^2y^2+64xy^3+16y^4$

Explanation:

Since ${(a + b)}^{4} = a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4}$ $(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4$ ,

then ${(2 x + 2 y)}^{4} = {(2 x)}^{4} + 4 {(2 x)}^{3} (2 y) + 6 {(2 x)}^{2} {(2 y)}^{2} + 4 (2 x) {(2 y)}^{3} + {(2 y)}^{4}$ $(2x+2y)^4=(2x)^4+4(2x)^3(2y)+6(2x)^2(2y)^2+4(2x)(2y)^3+(2y)^4$

that is

$16 x^{4} + 64 x^{3} y + 96 x^{2} y^{2} + 64 x y^{3} + 16 y^{4}$ $16x^4+64x^3y+96x^2y^2+64xy^3+16y^4$

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How do you expand ${(2 x + 2 y)}^{4}$ $(2x+2y)^4$ ?

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