Find the Product f(x)=x , g(x)=x^3-1

$f (x) = x$ , $g (x) = x^{3} - 1$

Step 1

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

$(x) \cdot (x^{3} - 1)$

Step 2

Simplify.

Apply the distributive property.

$x \cdot x^{3} + x \cdot - 1$

Multiply $x$ by $x^{3}$ by adding the exponents.

Multiply $x$ by $x^{3}$ .

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

$x^{1} x^{3} + x \cdot - 1$

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

$x^{1 + 3} + x \cdot - 1$

Add $1$ and $3$ .

$x^{4} + x \cdot - 1$

Move $- 1$ to the left of $x$ .

$x^{4} - 1 \cdot x$

Rewrite $- 1 x$ as $- x$ .

$x^{4} - x$