Simplify 2p(p^2-6p+1)

$2 p (p^{2} - 6 p + 1)$

Step 1

Apply the distributive property.

$2 p \cdot p^{2} + 2 p (- 6 p) + 2 p \cdot 1$

Step 2

Simplify.

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

Move $p^{2}$ .

$2 (p^{2} p) + 2 p (- 6 p) + 2 p \cdot 1$

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

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

$2 (p^{2} p^{1}) + 2 p (- 6 p) + 2 p \cdot 1$

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

$2 p^{2 + 1} + 2 p (- 6 p) + 2 p \cdot 1$

Add $2$ and $1$ .

$2 p^{3} + 2 p (- 6 p) + 2 p \cdot 1$

Rewrite using the commutative property of multiplication.

$2 p^{3} + 2 \cdot - 6 p \cdot p + 2 p \cdot 1$

Multiply $2$ by $1$ .

$2 p^{3} + 2 \cdot - 6 p \cdot p + 2 p$

Step 3

Simplify each term.

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$2 p^{3} + 2 \cdot - 6 (p \cdot p) + 2 p$

Multiply $p$ by $p$ .

$2 p^{3} + 2 \cdot - 6 p^{2} + 2 p$

Multiply $2$ by $- 6$ .

$2 p^{3} - 12 p^{2} + 2 p$