Find the Product (w+5)(w^2+3w)

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

Expand $(w + 5) (w^{2} + 3 w)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

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

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

$w^{1} w^{2} + w (3 w) + 5 w^{2} + 5 (3 w)$

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

$w^{1 + 2} + w (3 w) + 5 w^{2} + 5 (3 w)$

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $w$ by $w$ by adding the exponents.

Move $w$ .

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

Multiply $w$ by $w$ .

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

Multiply $3$ by $5$ .

$w^{3} + 3 w^{2} + 5 w^{2} + 15 w$

Add $3 w^{2}$ and $5 w^{2}$ .

$w^{3} + 8 w^{2} + 15 w$