Find the Product f(x)=5x+1 , g(x)=x^2-x

$f (x) = 5 x + 1$ , $g (x) = x^{2} - x$

Step 1

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

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

Step 2

Simplify.

Expand $(5 x + 1) (x^{2} - x)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

$5 x^{3} + 5 x (- x) + 1 x^{2} + 1 (- x)$

Rewrite using the commutative property of multiplication.

$5 x^{3} + 5 \cdot - 1 x \cdot x + 1 x^{2} + 1 (- x)$

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

Move $x$ .

$5 x^{3} + 5 \cdot - 1 (x \cdot x) + 1 x^{2} + 1 (- x)$

Multiply $x$ by $x$ .

$5 x^{3} + 5 \cdot - 1 x^{2} + 1 x^{2} + 1 (- x)$

Multiply $5$ by $- 1$ .

$5 x^{3} - 5 x^{2} + 1 x^{2} + 1 (- x)$

Multiply $x^{2}$ by $1$ .

$5 x^{3} - 5 x^{2} + x^{2} + 1 (- x)$

Multiply $- x$ by $1$ .

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

Add $- 5 x^{2}$ and $x^{2}$ .

$5 x^{3} - 4 x^{2} - x$