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

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

Step 1

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

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

Step 2

Simplify.

Apply the distributive property.

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

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

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

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

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

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

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

Add $2$ and $1$ .

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

Move $- 5$ to the left of $x^{2}$ .

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