What is expand (V(p+h)(Vp-Vh)(h-p))/(p^2) ?

The solution to expand (V(p+h)(Vp-Vh)(h-p))/(p^2) is V^2h-V^2p-(V^2h^3}{p^2}+\frac{V^2h^2)/p

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expand (V(p+h)(Vp-Vh)(h-p))/(p^2)

expand

\frac{V ( p + h ) ( V p - Vh ) ( h - p )}{p ^{2}}

V^{2} h - V^{2} p - \frac{V ^{2} h ^{3}}{p ^{2}} + \frac{V ^{2} h ^{2}}{p}

Solution steps

\frac{V ( p + h ) ( V p - Vh ) ( h - p )}{p ^{2}}

Expand

V (p + h) (V p - Vh) (h - p) : V^{2} p^{2} h - V^{2} p^{3} - V^{2} h^{3} + V^{2} p h^{2}

= \frac{V ^{2} p ^{2} h - V ^{2} p ^{3} - V ^{2} h ^{3} + V ^{2} p h ^{2}}{p ^{2}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{V ^{2} p ^{2} h - V ^{2} p ^{3} - V ^{2} h ^{3} + V ^{2} p h ^{2}}{p ^{2}} = \frac{V ^{2} p ^{2} h}{p ^{2}} - \frac{V ^{2} p ^{3}}{p ^{2}} - \frac{V ^{2} h ^{3}}{p ^{2}} + \frac{V ^{2} p h ^{2}}{p ^{2}}

= \frac{V ^{2} p ^{2} h}{p ^{2}} - \frac{V ^{2} p ^{3}}{p ^{2}} - \frac{V ^{2} h ^{3}}{p ^{2}} + \frac{V ^{2} p h ^{2}}{p ^{2}}

Cancel

\frac{V ^{2} p ^{2} h}{p ^{2}} : V^{2} h

= V^{2} h - \frac{V ^{2} p ^{3}}{p ^{2}} - \frac{V ^{2} h ^{3}}{p ^{2}} + \frac{V ^{2} p h ^{2}}{p ^{2}}

Cancel

\frac{V ^{2} p ^{3}}{p ^{2}} : V^{2} p

= V^{2} h - V^{2} p - \frac{V ^{2} h ^{3}}{p ^{2}} + \frac{V ^{2} p h ^{2}}{p ^{2}}

Cancel

\frac{V ^{2} p h ^{2}}{p ^{2}} : \frac{V ^{2} h ^{2}}{p}

= V^{2} h - V^{2} p - \frac{V ^{2} h ^{3}}{p ^{2}} + \frac{V ^{2} h ^{2}}{p}

λ e^{λ t} g (e^{t} - λ e^{t})

\frac{15 a}{s ( 3 s + 8 )}

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

x (1 + x ln (x y - 5))

\frac{5}{6} - 2

What is expand (V(p+h)(Vp-Vh)(h-p))/(p^2) ?
The solution to expand (V(p+h)(Vp-Vh)(h-p))/(p^2) is V^2h-V^2p-(V^2h^3}{p^2}+\frac{V^2h^2)/p