Simplify b(b^2-12b+1)

$b (b^{2} - 12 b + 1)$

Step 1

Apply the distributive property.

$b \cdot b^{2} + b (- 12 b) + b \cdot 1$

Step 2

Simplify.

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

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

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

$b^{1} b^{2} + b (- 12 b) + b \cdot 1$

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

$b^{1 + 2} + b (- 12 b) + b \cdot 1$

Add $1$ and $2$ .

$b^{3} + b (- 12 b) + b \cdot 1$

Rewrite using the commutative property of multiplication.

$b^{3} - 12 b \cdot b + b \cdot 1$

Multiply $b$ by $1$ .

$b^{3} - 12 b \cdot b + b$

Step 3

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$b^{3} - 12 (b \cdot b) + b$

Multiply $b$ by $b$ .

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