What is (-3v+w)v(v+w)+(4w-v)v(v-w)-w(v+w)(v-w) ?

The solution to (-3v+w)v(v+w)+(4w-v)v(v-w)-w(v+w)(v-w) is -4v^3+w^3+2wv^2-3vw^2

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simplify (-3v+w)v(v+w)+(4w-v)v(v-w)-w(v+w)(v-w)

simplify

(- 3 v + w) v (v + w) + (4 w - v) v (v - w) - w (v + w) (v - w)

- 4 v^{3} + w^{3} + 2 w v^{2} - 3 v w^{2}

Solution steps

(- 3 v + w) v (v + w) + (4 w - v) v (v - w) - w (v + w) (v - w)

= v (- 3 v + w) (v + w) + v (4 w - v) (v - w) - w (v + w) (v - w)

Expand

v (- 3 v + w) (v + w) : - 3 v^{3} - 2 w v^{2} + v w^{2}

= - 3 v^{3} - 2 w v^{2} + v w^{2} + v (4 w - v) (v - w) - w (v + w) (v - w)

Expand

v (4 w - v) (v - w) : - 4 v w^{2} - v^{3} + 5 w v^{2}

= - 3 v^{3} - 2 w v^{2} + v w^{2} - 4 v w^{2} - v^{3} + 5 w v^{2} - w (v + w) (v - w)

Expand

- w (v + w) (v - w) : - w v^{2} + w^{3}

= - 3 v^{3} - 2 w v^{2} + v w^{2} - 4 v w^{2} - v^{3} + 5 w v^{2} - w v^{2} + w^{3}

Add similar elements:

v w^{2} - 4 v w^{2} = - 3 v w^{2}

= - 3 v^{3} - 2 w v^{2} - 3 v w^{2} - v^{3} + 5 w v^{2} - w v^{2} + w^{3}

Group like terms

= - 3 v^{3} - v^{3} + w^{3} - 2 w v^{2} + 5 w v^{2} - w v^{2} - 3 v w^{2}

Add similar elements:

- 3 v^{3} - v^{3} = - 4 v^{3}

= - 4 v^{3} + w^{3} - 2 w v^{2} + 5 w v^{2} - w v^{2} - 3 v w^{2}

Add similar elements:

- 2 w v^{2} + 5 w v^{2} - w v^{2} = 2 w v^{2}

= - 4 v^{3} + w^{3} + 2 w v^{2} - 3 v w^{2}

lo g_{10} (\frac{a ^{2}}{2 a ^{\frac{1}{2}}})

(2 x + 7) (x - 3)

\frac{2 ^{3}}{3 !}

(y + 3) (y + 5)

4 x (- 5 x^{2} + 3 x - 2) + (x^{2} - 3 x + 1) (x^{2} - 3)

What is (-3v+w)v(v+w)+(4w-v)v(v-w)-w(v+w)(v-w) ?
The solution to (-3v+w)v(v+w)+(4w-v)v(v-w)-w(v+w)(v-w) is -4v^3+w^3+2wv^2-3vw^2