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

The solution to x^2*(x+y)^3-2x*y^2*(x+y)^2 is x^5-3x^2y^3+3x^4y+x^3y^2-2xy^4

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

simplify

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

x^{5} - 3 x^{2} y^{3} + 3 x^{4} y + x^{3} y^{2} - 2 x y^{4}

Solution steps

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

Expand

x^{2} (x + y)^{3} : x^{5} + 3 x^{4} y + 3 x^{3} y^{2} + x^{2} y^{3}

= x^{5} + 3 x^{4} y + 3 x^{3} y^{2} + x^{2} y^{3} - 2 x y^{2} (x + y)^{2}

Expand

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

= x^{5} + 3 x^{4} y + 3 x^{3} y^{2} + x^{2} y^{3} - 2 x^{3} y^{2} - 4 x^{2} y^{3} - 2 x y^{4}

Group like terms

= x^{5} + x^{2} y^{3} - 4 x^{2} y^{3} + 3 x^{4} y + 3 x^{3} y^{2} - 2 x^{3} y^{2} - 2 x y^{4}

Add similar elements:

x^{2} y^{3} - 4 x^{2} y^{3} = - 3 x^{2} y^{3}

= x^{5} - 3 x^{2} y^{3} + 3 x^{4} y + 3 x^{3} y^{2} - 2 x^{3} y^{2} - 2 x y^{4}

Add similar elements:

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

= x^{5} - 3 x^{2} y^{3} + 3 x^{4} y + x^{3} y^{2} - 2 x y^{4}

(\frac{1}{3} a + \frac{1}{4} b)^{2}

9 x^{3} - 6 x^{2} + 12 x^{5} - 18 x^{7}

(x - 1)^{2} (x + 1)^{3} (x - 4) 0

a^{8} + a^{4} - 2

4 a^{4} + 16 a^{2} b^{2} + 16 b^{4}

What is x^2*(x+y)^3-2x*y^2*(x+y)^2 ?
The solution to x^2*(x+y)^3-2x*y^2*(x+y)^2 is x^5-3x^2y^3+3x^4y+x^3y^2-2xy^4