What is expand (2y'(x)-4)(y+2x) ?

The solution to expand (2y'(x)-4)(y+2x) is 2y'(x)y+4xy'(x)-4y-8x

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expand (2y'(x)-4)(y+2x)

expand

(2 y^{'} (x) - 4) (y + 2 x)

2 y' (x) y + 4 x y' (x) - 4 y - 8 x

Solution steps

(2 y^{'} (x) - 4) (y + 2 x)

Apply FOIL method:

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

a = 2 y^{'} (x), b = - 4, c = y, d = 2 x

= 2 y^{^{'}} (x) y + 2 y^{^{'}} (x) 2 x + (- 4) y + (- 4) \cdot 2 x

Apply minus-plus rules

+ (- a) = - a

= 2 y^{^{'}} (x) y + 2 \cdot 2 x y^{^{'}} (x) - 4 y - 4 \cdot 2 x

Simplify

2 y^{'} (x) y + 2 \cdot 2 x y^{'} (x) - 4 y - 4 \cdot 2 x : 2 y^{'} (x) y + 4 x y^{'} (x) - 4 y - 8 x

= 2 y^{'} (x) y + 4 x y^{'} (x) - 4 y - 8 x

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

(n - k - 1)! \cdot (n - k)

What is expand (2y'(x)-4)(y+2x) ?
The solution to expand (2y'(x)-4)(y+2x) is 2y'(x)y+4xy'(x)-4y-8x