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

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

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

expand

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

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

Solution steps

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

Apply FOIL method:

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

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

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

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

\frac{25 ( 18 + x ^{25} )}{2}

y (x = 2 y - 4)

\frac{8}{s ( s + 2 ) ( s + 4 )}

\frac{4 ab + 2 ( a + b ) - b ^{2} + c}{a}

5 x \cdot 2 x

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