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

The solution to (x^2-3y)(x^3-5)+(x^2-3y)(y-x^3) is -5x^2+15y+x^2y-3y^2

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

simplify

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

- 5 x^{2} + 15 y + x^{2} y - 3 y^{2}

Solution steps

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

Expand

(x^{2} - 3 y) (x^{3} - 5) : x^{5} - 5 x^{2} - 3 x^{3} y + 15 y

= x^{5} - 5 x^{2} - 3 x^{3} y + 15 y + (x^{2} - 3 y) (y - x^{3})

Expand

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

= x^{5} - 5 x^{2} - 3 x^{3} y + 15 y + x^{2} y - x^{5} - 3 y^{2} + 3 x^{3} y

Group like terms

= x^{5} - x^{5} - 5 x^{2} - 3 x^{3} y + 3 x^{3} y + 15 y + x^{2} y - 3 y^{2}

Add similar elements:

x^{5} - x^{5} = 0

= - 5 x^{2} - 3 x^{3} y + 3 x^{3} y + 15 y + x^{2} y - 3 y^{2}

Add similar elements:

- 3 x^{3} y + 3 x^{3} y = 0

= - 5 x^{2} + 15 y + x^{2} y - 3 y^{2}

\frac{x}{( x ( 1 + x ) )}

8 x - 6 x

4 x^{3} + 12 x^{2} + 12 h + 4

x (x + 12)^{2}

\frac{( a ^{2} + a - 6 )}{( a + 3 )}

What is (x^2-3y)(x^3-5)+(x^2-3y)(y-x^3) ?
The solution to (x^2-3y)(x^3-5)+(x^2-3y)(y-x^3) is -5x^2+15y+x^2y-3y^2