What is expand (vy-y)(vdy+ydv) ?

The solution to expand (vy-y)(vdy+ydv) is v^2ydy+vy^2dv-vydy-y^2dv

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expand (vy-y)(vdy+ydv)

expand

(v y - y) (v d y + y d v)

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

Solution steps

(v y - y) (v d y + y d v)

Apply FOIL method:

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

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

= v y v d y + v yy d v + (- y) v d y + (- y) y d v

Apply minus-plus rules

+ (- a) = - a

= vv y d y + v yy d v - v y d y - yy d v

Simplify

vv y d y + v yy d v - v y d y - yy d v : v^{2} y d y + v y^{2} d v - v y d y - y^{2} d v

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

\frac{4 !}{3 ! \cdot ( 1 - ( 1 - x ) ) ^{3} \cdot ( 1 - ( 1 - x ) ) ^{1}}

(\frac{1}{6} d - \frac{1}{3} q)^{2}

\frac{( 0.5 + x ) ( 0.4 + x )}{( 0.5 - x ) ( 0.45 - x )}

(2 t + 1) (2 t)

What is expand (vy-y)(vdy+ydv) ?
The solution to expand (vy-y)(vdy+ydv) is v^2ydy+vy^2dv-vydy-y^2dv