Find the Product f(x)=5x-2 , g(x)=6x+3

$f (x) = 5 x - 2$ , $g (x) = 6 x + 3$

Step 1

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

$(5 x - 2) \cdot (6 x + 3)$

Step 2

Simplify.

Expand $(5 x - 2) (6 x + 3)$ using the FOIL Method.

Apply the distributive property.

$5 x (6 x + 3) - 2 (6 x + 3)$

Apply the distributive property.

$5 x (6 x) + 5 x \cdot 3 - 2 (6 x + 3)$

Apply the distributive property.

$5 x (6 x) + 5 x \cdot 3 - 2 (6 x) - 2 \cdot 3$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 6 x \cdot x + 5 x \cdot 3 - 2 (6 x) - 2 \cdot 3$

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

Move $x$ .

$5 \cdot 6 (x \cdot x) + 5 x \cdot 3 - 2 (6 x) - 2 \cdot 3$

Multiply $x$ by $x$ .

$5 \cdot 6 x^{2} + 5 x \cdot 3 - 2 (6 x) - 2 \cdot 3$

Multiply $5$ by $6$ .

$30 x^{2} + 5 x \cdot 3 - 2 (6 x) - 2 \cdot 3$

Multiply $3$ by $5$ .

$30 x^{2} + 15 x - 2 (6 x) - 2 \cdot 3$

Multiply $6$ by $- 2$ .

$30 x^{2} + 15 x - 12 x - 2 \cdot 3$

Multiply $- 2$ by $3$ .

$30 x^{2} + 15 x - 12 x - 6$

Subtract $12 x$ from $15 x$ .

$30 x^{2} + 3 x - 6$