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

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

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Answer 1 · 2018-06-20T18:47:35

$x^{4} + 4 x^{3} y + 6 x^{2} y^{2} + 4 x y^{3} + y^{4}$ $x^4+4x^3y+6x^2y^2+4xy^3+y^4$

Explanation:

since ${(x + y)}^{2} = x^{2} + 2 x y + y^{2}$ $(x+y)^2=x^2+2xy+y^2$
we can write

$(x^{2} + 2 x y + y^{2}) (x^{2} + 2 x y + y^{2}) = x^{4} + x^{2} y^{2} + 2 x^{3} y + x^{2} y^{2} + y^{4} + 2 x y^{3} + 2 x^{3} y + 2 x y^{3} + 4 x^{2} y^{2}$ $(x^2+2xy+y^2)(x^2+2xy+y^2)=x^4+x^2y^2+2x^3y+x^2y^2+y^4+2xy^3+2x^3y+2xy^3+4x^2y^2$
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How do you expand ${(y + x)}^{4}$ $(y+x)^4$ ?

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