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 yc x + b y d y

= 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

\frac{2 ( x ^{2} - 9 )}{x ^{2} - 4}

\frac{x ^{2} + 5}{( x - 1 ) ( x ^{2} + 4 ) ^{2}}

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

\frac{5 x ^{2} - 36 x + 48}{x ( x - 4 ) ^{2}}

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

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