Simplify (3w+1)(w^2-4w+2)

$(3 w + 1) (w^{2} - 4 w + 2)$

Step 1

Expand $(3 w + 1) (w^{2} - 4 w + 2)$ by multiplying each term in the first expression by each term in the second expression.

$3 w \cdot w^{2} + 3 w (- 4 w) + 3 w \cdot 2 + 1 w^{2} + 1 (- 4 w) + 1 \cdot 2$

Step 2

Simplify terms.

Simplify each term.

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

Move $w^{2}$ .

$3 (w^{2} w) + 3 w (- 4 w) + 3 w \cdot 2 + 1 w^{2} + 1 (- 4 w) + 1 \cdot 2$

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

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

$3 (w^{2} w^{1}) + 3 w (- 4 w) + 3 w \cdot 2 + 1 w^{2} + 1 (- 4 w) + 1 \cdot 2$

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

$3 w^{2 + 1} + 3 w (- 4 w) + 3 w \cdot 2 + 1 w^{2} + 1 (- 4 w) + 1 \cdot 2$

Add $2$ and $1$ .

$3 w^{3} + 3 w (- 4 w) + 3 w \cdot 2 + 1 w^{2} + 1 (- 4 w) + 1 \cdot 2$

Rewrite using the commutative property of multiplication.

$3 w^{3} + 3 \cdot - 4 w \cdot w + 3 w \cdot 2 + 1 w^{2} + 1 (- 4 w) + 1 \cdot 2$

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

Move $w$ .

$3 w^{3} + 3 \cdot - 4 (w \cdot w) + 3 w \cdot 2 + 1 w^{2} + 1 (- 4 w) + 1 \cdot 2$

Multiply $w$ by $w$ .

$3 w^{3} + 3 \cdot - 4 w^{2} + 3 w \cdot 2 + 1 w^{2} + 1 (- 4 w) + 1 \cdot 2$

Multiply $3$ by $- 4$ .

$3 w^{3} - 12 w^{2} + 3 w \cdot 2 + 1 w^{2} + 1 (- 4 w) + 1 \cdot 2$

Multiply $2$ by $3$ .

$3 w^{3} - 12 w^{2} + 6 w + 1 w^{2} + 1 (- 4 w) + 1 \cdot 2$

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

$3 w^{3} - 12 w^{2} + 6 w + w^{2} + 1 (- 4 w) + 1 \cdot 2$

Multiply $- 4 w$ by $1$ .

$3 w^{3} - 12 w^{2} + 6 w + w^{2} - 4 w + 1 \cdot 2$

Multiply $2$ by $1$ .

$3 w^{3} - 12 w^{2} + 6 w + w^{2} - 4 w + 2$

Simplify by adding terms.

Add $- 12 w^{2}$ and $w^{2}$ .

$3 w^{3} - 11 w^{2} + 6 w - 4 w + 2$

Subtract $4 w$ from $6 w$ .

$3 w^{3} - 11 w^{2} + 2 w + 2$