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

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

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

expand

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

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

Solution steps

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

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

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

1 7^{(k + 1)} - 9^{(k + 1)}

2 x y^{2} (3 x y - 4 x + 8)^{2} + 7 x - 10

\frac{( - x + 15 ) ( - x + 5 )}{2}

- 4 (x + h) - 1

\frac{( 2 x - 1 )}{s ^{2} ( s + 1 ) ^{3}}

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