What is expand (mv-v)(mdv+vdm) ?

The solution to expand (mv-v)(mdv+vdm) is m^2vdv+mv^2dm-mvdv-v^2dm

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expand (mv-v)(mdv+vdm)

expand

(m v - v) (m d v + v d m)

m^{2} v d v + m v^{2} d m - m v d v - v^{2} d m

Solution steps

(m v - v) (m d v + v d m)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = m v, b = - v, c = m d v, d = v d m

= m v m d v + m vv d m + (- v) m d v + (- v) v d m

Apply minus-plus rules

+ (- a) = - a

= mm v d v + m vv d m - m v d v - vv d m

Simplify

mm v d v + m vv d m - m v d v - vv d m : m^{2} v d v + m v^{2} d m - m v d v - v^{2} d m

= m^{2} v d v + m v^{2} d m - m v d v - v^{2} d m

\times (\times + 4 y)

\frac{d}{d v} ((p) ((p + \frac{5}{v ^{2}}) (v - 3.1)))

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

l im x \Rightarrow 5 (x^{2} - x - 20 x^{2} - 7 x + 10)

\frac{( x + h ) y ^{3} - ( x + h ) ^{3} y}{h}

What is expand (mv-v)(mdv+vdm) ?
The solution to expand (mv-v)(mdv+vdm) is m^2vdv+mv^2dm-mvdv-v^2dm