Simplify b(b-3)^2

$b {(b - 3)}^{2}$

Step 1

Rewrite ${(b - 3)}^{2}$ as $(b - 3) (b - 3)$ .

$b ((b - 3) (b - 3))$

Step 2

Expand $(b - 3) (b - 3)$ using the FOIL Method.

Apply the distributive property.

$b (b (b - 3) - 3 (b - 3))$

Apply the distributive property.

$b (b \cdot b + b \cdot - 3 - 3 (b - 3))$

Apply the distributive property.

$b (b \cdot b + b \cdot - 3 - 3 b - 3 \cdot - 3)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $b$ by $b$ .

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

Move $- 3$ to the left of $b$ .

$b (b^{2} - 3 \cdot b - 3 b - 3 \cdot - 3)$

Multiply $- 3$ by $- 3$ .

$b (b^{2} - 3 b - 3 b + 9)$

Subtract $3 b$ from $- 3 b$ .

$b (b^{2} - 6 b + 9)$

Step 4

Apply the distributive property.

$b \cdot b^{2} + b (- 6 b) + b \cdot 9$

Step 5

Simplify.

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

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

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

$b^{1} b^{2} + b (- 6 b) + b \cdot 9$

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

$b^{1 + 2} + b (- 6 b) + b \cdot 9$

Add $1$ and $2$ .

$b^{3} + b (- 6 b) + b \cdot 9$

Rewrite using the commutative property of multiplication.

$b^{3} - 6 b \cdot b + b \cdot 9$

Move $9$ to the left of $b$ .

$b^{3} - 6 b \cdot b + 9 \cdot b$

Step 6

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

Move $b$ .

$b^{3} - 6 (b \cdot b) + 9 \cdot b$

Multiply $b$ by $b$ .

$b^{3} - 6 b^{2} + 9 \cdot b$

$b^{3} - 6 b^{2} + 9 b$

Simplify b(b-3)^2

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