What is expand (2(y*v)+4y)(dy*v) ?

The solution to expand (2(y*v)+4y)(dy*v) is 2v^2ydy+4vydy

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expand (2(yv)+4y)(dyv)

expand

(2 (y \cdot v) + 4 y) (d y \cdot v)

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

Solution steps

(2 (y v) + 4 y) (d y v)

= (2 (v y) + 4 y) (v d y)

Apply the distributive law:

a (b + c) = ab + a c

a = (d y v), b = 2 (y v), c = 4 y

= (d y v) \cdot 2 (y v) + (d y v) \cdot 4 y

= 2 (v d y) (v y) + 4 y (v d y)

Simplify

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

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

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What is expand (2(y*v)+4y)(dy*v) ?
The solution to expand (2(y*v)+4y)(dy*v) is 2v^2ydy+4vydy