What is expand (6x-2y)(3-y'(x)) ?

The solution to expand (6x-2y)(3-y'(x)) is 18x-6xy'(x)-6y+2yy'(x)

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expand (6x-2y)(3-y'(x))

expand

(6 x - 2 y) (3 - y^{'} (x))

18 x - 6 x y' (x) - 6 y + 2 yy' (x)

Solution steps

(6 x - 2 y) (3 - y^{'} (x))

Apply FOIL method:

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

a = 6 x, b = - 2 y, c = 3, d = - y^{'} (x)

= 6 x \cdot 3 + 6 x (- y^{^{'}} (x)) + (- 2 y) \cdot 3 + (- 2 y) (- y^{^{'}} (x))

Apply minus-plus rules

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

= 6 \cdot 3 x - 6 x y^{^{'}} (x) - 2 \cdot 3 y + 2 y y^{^{'}} (x)

Simplify

6 \cdot 3 x - 6 x y^{'} (x) - 2 \cdot 3 y + 2 y y^{'} (x) : 18 x - 6 x y^{'} (x) - 6 y + 2 y y^{'} (x)

= 18 x - 6 x y^{'} (x) - 6 y + 2 y y^{'} (x)

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

\frac{x - 5}{( x - 9 ) ( x + 8 )}

3 (7 - 9 k + 23 k = 4 k - (24 - k))

(x - 75) (tan (3 5^{\circ}))

3 ((1^{2}) (b))

What is expand (6x-2y)(3-y'(x)) ?
The solution to expand (6x-2y)(3-y'(x)) is 18x-6xy'(x)-6y+2yy'(x)