What is expand (2vy-3y)(vdy+ydv) ?

The solution to expand (2vy-3y)(vdy+ydv) is 2v^2ydy+2vy^2dv-3vydy-3y^2dv

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expand (2vy-3y)(vdy+ydv)

expand

(2 v y - 3 y) (v d y + y d v)

2 v^{2} y d y + 2 v y^{2} d v - 3 v y d y - 3 y^{2} d v

Solution steps

(2 v y - 3 y) (v d y + y d v)

Apply FOIL method:

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

a = 2 v y, b = - 3 y, c = v d y, d = y d v

= 2 v y v d y + 2 v yy d v + (- 3 y) v d y + (- 3 y) y d v

Apply minus-plus rules

+ (- a) = - a

= 2 vv y d y + 2 v yy d v - 3 v y d y - 3 yy d v

Simplify

2 vv y d y + 2 v yy d v - 3 v y d y - 3 yy d v : 2 v^{2} y d y + 2 v y^{2} d v - 3 v y d y - 3 y^{2} d v

= 2 v^{2} y d y + 2 v y^{2} d v - 3 v y d y - 3 y^{2} d v

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

\frac{8 ( 3 x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}}

\frac{1}{3} H (t - 6) - \frac{1}{3} e^{- 3 (t - 6)}

\frac{20 ( s + 1 ) ( s + 2 )}{s ^{2} + 32 s + 40}

(x - 4) (x - 6) (x + 7)

What is expand (2vy-3y)(vdy+ydv) ?
The solution to expand (2vy-3y)(vdy+ydv) is 2v^2ydy+2vy^2dv-3vydy-3y^2dv