Find the Product f(x)=2x+3 g(x)=5x^2

$f (x) = 2 x + 3$ $g (x) = 5 x^{2}$

Step 1

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

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

Step 2

Simplify.

Simplify by multiplying through.

Apply the distributive property.

$2 x (5 x^{2}) + 3 (5 x^{2})$

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Multiply $5$ by $3$ .

$2 \cdot 5 x \cdot x^{2} + 15 x^{2}$

Simplify each term.

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$2 \cdot 5 (x^{2} x) + 15 x^{2}$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$2 \cdot 5 (x^{2} x^{1}) + 15 x^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot 5 x^{2 + 1} + 15 x^{2}$

Add $2$ and $1$ .

$2 \cdot 5 x^{3} + 15 x^{2}$

Multiply $2$ by $5$ .

$10 x^{3} + 15 x^{2}$