What is expand (acx^2-by)(cx+dy) ?

The solution to expand (acx^2-by)(cx+dy) is ac^2x^3+acx^2dy-cbxy-bydy

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expand (acx^2-by)(cx+dy)

expand

(a c x^{2} - b y) (c x + d y)

a c^{2} x^{3} + a c x^{2} d y - c b x y - b y d y

Solution steps

(a c x^{2} - b y) (c x + d y)

Apply FOIL method:

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

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

= a c x^{2} c x + a c x^{2} d y + (- b y) c x + (- b y) d y

Apply minus-plus rules

+ (- a) = - a

= a cc x^{2} x + a c x^{2} d y - c b x y - b y d y

a cc x^{2} x = a c^{2} x^{3}

= a c^{2} x^{3} + a c x^{2} d y - c b x y - b y d y

(x tan (\frac{y}{x}) + y) d x - x d y

, (x + 1) (x - 7)

- 5 (- 3 s = 9 s + 9) - 2 s

(1 - v) (4 + v) d x

(2 x + sin (3 x)) d x

What is expand (acx^2-by)(cx+dy) ?
The solution to expand (acx^2-by)(cx+dy) is ac^2x^3+acx^2dy-cbxy-bydy