What is expand (4v^2y^2+2y^2)(vdy+ydv) ?

The solution to expand (4v^2y^2+2y^2)(vdy+ydv) is 4v^3y^2dy+4v^2y^3dv+2vy^2dy+2y^3dv

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expand (4v^2y^2+2y^2)(vdy+ydv)

expand

(4 v^{2} y^{2} + 2 y^{2}) (v d y + y d v)

4 v^{3} y^{2} d y + 4 v^{2} y^{3} d v + 2 v y^{2} d y + 2 y^{3} d v

Solution steps

(4 v^{2} y^{2} + 2 y^{2}) (v d y + y d v)

Apply FOIL method:

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

a = 4 v^{2} y^{2}, b = 2 y^{2}, c = v d y, d = y d v

= 4 v^{2} y^{2} v d y + 4 v^{2} y^{2} y d v + 2 y^{2} v d y + 2 y^{2} y d v

= 4 v^{2} v y^{2} d y + 4 v^{2} y^{2} y d v + 2 v y^{2} d y + 2 y^{2} y d v

Simplify

4 v^{2} v y^{2} d y + 4 v^{2} y^{2} y d v + 2 v y^{2} d y + 2 y^{2} y d v : 4 v^{3} y^{2} d y + 4 v^{2} y^{3} d v + 2 v y^{2} d y + 2 y^{3} d v

= 4 v^{3} y^{2} d y + 4 v^{2} y^{3} d v + 2 v y^{2} d y + 2 y^{3} d v

\frac{a + bi}{( a - bi ) ^{2}}

\frac{2 ( x - 2 )}{5}

y (a - b y^{2}) d y

7 pp

y Q_{0} (1 - e^{- \frac{y}{a}})

What is expand (4v^2y^2+2y^2)(vdy+ydv) ?
The solution to expand (4v^2y^2+2y^2)(vdy+ydv) is 4v^3y^2dy+4v^2y^3dv+2vy^2dy+2y^3dv