What is (((x+y)^3-2y*(y+x)^2))/((x^2+y^2)) ?

The solution to (((x+y)^3-2y*(y+x)^2))/((x^2+y^2)) is (x^3+x^2y-xy^2-y^3)/(x^2+y^2)

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simplify (((x+y)^3-2y*(y+x)^2))/((x^2+y^2))

simplify

\frac{( ( x + y ) ^{3} - 2 y \cdot ( y + x ) ^{2} )}{( x ^{2} + y ^{2} )}

\frac{x ^{3} + x ^{2} y - x y ^{2} - y ^{3}}{x ^{2} + y ^{2}}

Solution steps

\frac{( x + y ) ^{3} - 2 y ( y + x ) ^{2}}{x ^{2} + y ^{2}}

Expand

(x + y)^{3} : x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}

= \frac{x ^{3} + 3 x ^{2} y + 3 x y ^{2} + y ^{3} - 2 y ( y + x ) ^{2}}{x ^{2} + y ^{2}}

Expand

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

= \frac{x ^{3} + 3 x ^{2} y + 3 x y ^{2} + y ^{3} - 2 y ^{3} - 4 x y ^{2} - 2 x ^{2} y}{x ^{2} + y ^{2}}

Simplify

x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 2 y^{3} - 4 x y^{2} - 2 x^{2} y : x^{3} + x^{2} y - x y^{2} - y^{3}

= \frac{x ^{3} + x ^{2} y - x y ^{2} - y ^{3}}{x ^{2} + y ^{2}}

16 x^{3} \cdot y^{2} - 8 x^{4} \cdot y - 24 x^{2} \cdot y - 40 x^{2} \cdot y^{3}

4 + 5 (x)

8.25 m + 6 m - 2 m

\frac{1}{2} a - \frac{3}{4} a

2 (y + 3)

What is (((x+y)^3-2y*(y+x)^2))/((x^2+y^2)) ?
The solution to (((x+y)^3-2y*(y+x)^2))/((x^2+y^2)) is (x^3+x^2y-xy^2-y^3)/(x^2+y^2)