Find the Product f(x)=-7x-9 , g(x)=-3x+10

$f (x) = - 7 x - 9$ , $g (x) = - 3 x + 10$

Step 1

Replace the function designators with the actual functions in $f (x) \cdot (g (x))$ .

$(- 7 x - 9) \cdot (- 3 x + 10)$

Step 2

Simplify.

Expand $(- 7 x - 9) (- 3 x + 10)$ using the FOIL Method.

Apply the distributive property.

$- 7 x (- 3 x + 10) - 9 (- 3 x + 10)$

Apply the distributive property.

$- 7 x (- 3 x) - 7 x \cdot 10 - 9 (- 3 x + 10)$

Apply the distributive property.

$- 7 x (- 3 x) - 7 x \cdot 10 - 9 (- 3 x) - 9 \cdot 10$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 7 \cdot - 3 x \cdot x - 7 x \cdot 10 - 9 (- 3 x) - 9 \cdot 10$

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

Move $x$ .

$- 7 \cdot - 3 (x \cdot x) - 7 x \cdot 10 - 9 (- 3 x) - 9 \cdot 10$

Multiply $x$ by $x$ .

$- 7 \cdot - 3 x^{2} - 7 x \cdot 10 - 9 (- 3 x) - 9 \cdot 10$

Multiply $- 7$ by $- 3$ .

$21 x^{2} - 7 x \cdot 10 - 9 (- 3 x) - 9 \cdot 10$

Multiply $10$ by $- 7$ .

$21 x^{2} - 70 x - 9 (- 3 x) - 9 \cdot 10$

Multiply $- 3$ by $- 9$ .

$21 x^{2} - 70 x + 27 x - 9 \cdot 10$

Multiply $- 9$ by $10$ .

$21 x^{2} - 70 x + 27 x - 90$

Add $- 70 x$ and $27 x$ .

$21 x^{2} - 43 x - 90$