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

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

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

expand

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

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

Solution steps

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

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

Simplify

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

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

(5 x + 8 (\frac{d y}{d x}))^{2}

(x^{2} - x y + y^{2})^{5}

\frac{( X - 6 )}{3 ( 4 - X )}

- 3 (e - e^{3})

\frac{y}{( s + x ) ( s + y )}

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