Find the Product f(x)=x-2 ; g(x)=5x^2

$f (x) = x - 2$ ; $g (x) = 5 x^{2}$

Step 1

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

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

Step 2

Simplify.

Apply the distributive property.

$x (5 x^{2}) - 2 (5 x^{2})$

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Multiply $5$ by $- 2$ .

$5 x \cdot x^{2} - 10 x^{2}$

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

Move $x^{2}$ .

$5 (x^{2} x) - 10 x^{2}$

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

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

$5 (x^{2} x^{1}) - 10 x^{2}$

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

$5 x^{2 + 1} - 10 x^{2}$

Add $2$ and $1$ .

$5 x^{3} - 10 x^{2}$