Evaluate Using the Given Value (ax+by)(cx-dy) , ad=bc , ac=18 , bd=50

$(a x + b y) (c x - d y)$ , $a d = b c$ , $a c = 18$ , $b d = 50$

Replace the variable $a d$ with $b c$ in the expression.

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

Expand $(a x + b y) (c x - d y)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$a (x \cdot x) c + a x (- d y) + b y (c x) + b y (- d y)$

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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