What is x(2x^2+3xy+y^2)-y(5x^2-2xy+y^2) ?

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

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simplify x(2x^2+3xy+y^2)-y(5x^2-2xy+y^2)

simplify

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

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

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

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

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

(7 - 5) (7 + 5)

cot^{2} (x) - cot^{2} (x) cos^{2} (x)

[\frac{2 x - 2 y ^{2} \cdot ( - x ) 2}{( 2 y ^{4} ) 4}] 4

\frac{2 ^{4}}{( - 4 ) + 25 \cdot 4 + ( 3 \cdot 3 - 5 ) ^{2}}

(3 + 4 i) + (5 - 2 i)

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