What is expand (6x-2y)(6-2y'(x)) ?

The solution to expand (6x-2y)(6-2y'(x)) is 36x-12xy'(x)-12y+4yy'(x)

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expand (6x-2y)(6-2y'(x))

expand

(6 x - 2 y) (6 - 2 y^{'} (x))

36 x - 12 x y' (x) - 12 y + 4 yy' (x)

Solution steps

(6 x - 2 y) (6 - 2 y^{'} (x))

Apply FOIL method:

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

a = 6 x, b = - 2 y, c = 6, d = - 2 y^{'} (x)

= 6 x \cdot 6 + 6 x (- 2 y^{^{'}} (x)) + (- 2 y) \cdot 6 + (- 2 y) (- 2 y^{^{'}} (x))

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= 6 \cdot 6 x - 6 \cdot 2 x y^{^{'}} (x) - 2 \cdot 6 y + 2 \cdot 2 y y^{^{'}} (x)

Simplify

6 \cdot 6 x - 6 \cdot 2 x y^{'} (x) - 2 \cdot 6 y + 2 \cdot 2 y y^{'} (x) : 36 x - 12 x y^{'} (x) - 12 y + 4 y y^{'} (x)

= 36 x - 12 x y^{'} (x) - 12 y + 4 y y^{'} (x)

\frac{2 b x}{( a + b x ) ^{2}}

\frac{2}{3} (3 x + 9 = - 2) (2 x + 6)

\frac{( x - 5 ) ( x + 1 ) ( x - 1 )}{3 x + 2}

(- \frac{1}{x ^{2}})^{8}

P (8, - 7) Q (13, 7)

What is expand (6x-2y)(6-2y'(x)) ?
The solution to expand (6x-2y)(6-2y'(x)) is 36x-12xy'(x)-12y+4yy'(x)