What is expand (ax-by)(cx+dy) ?

The solution to expand (ax-by)(cx+dy) is acx^2+axdy-bcxy-bydy

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expand (ax-by)(cx+dy)

expand

(a x - b y) (c x + d y)

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

Solution steps

(a x - b y) (c x + d y)

Apply FOIL method:

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

a = a x, b = - b y, c = c x, d = d y

= a x c x + a x d y + (- b y) c x + (- b y) d y

Apply minus-plus rules

+ (- a) = - a

= a c xx + a x d y - b c x y - b y d y

a c xx = a c x^{2}

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

(5 + 5 i)^{5}

\frac{10}{( x + 2 ) ^{2}}

\frac{d ^{2}}{d x ^{2}} ((2 x + 1)^{4}) + 8 x (2 x + 1)^{3}

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

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

What is expand (ax-by)(cx+dy) ?
The solution to expand (ax-by)(cx+dy) is acx^2+axdy-bcxy-bydy