What is x^2(x+y)+2x(x^2+y) ?

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

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simplify x^2(x+y)+2x(x^2+y)

simplify

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

3 x^{3} + x^{2} y + 2 x y

Solution steps

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

Expand

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

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

Expand

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

= x^{3} + x^{2} y + 2 x^{3} + 2 x y

Group like terms

= x^{3} + 2 x^{3} + x^{2} y + 2 x y

Add similar elements:

x^{3} + 2 x^{3} = 3 x^{3}

= 3 x^{3} + x^{2} y + 2 x y

\frac{( 4 x ^{2} - 49 )}{( 2 x + 7 )} - \frac{( x ^{2} - 16 x + 64 )}{( 8 - x )} + \frac{( 9 x ^{2} - 6 x + 1 )}{( 1 - 3 x )}

3 x^{2} y^{3} - 6 x^{3} y^{4} + 12 x y

x^{4} + 8 x y^{3}

(\frac{a ^{2}}{4})^{2}

\frac{\frac{1}{x ^{2}}}{( 1 + \frac{1}{x ^{2}} ) ^{\frac{3}{2}}}

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