Find the Product (a-b)^3

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Rewrite using the commutative property of multiplication.

$a^{3} + 3 \cdot - 1 a^{2} b + 3 a {(- b)}^{2} + {(- b)}^{3}$

Multiply $3$ by $- 1$ .

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

Apply the product rule to $- b$ .

$a^{3} - 3 a^{2} b + 3 a ({(- 1)}^{2} b^{2}) + {(- b)}^{3}$

Rewrite using the commutative property of multiplication.

$a^{3} - 3 a^{2} b + 3 \cdot {(- 1)}^{2} a b^{2} + {(- b)}^{3}$

Raise $- 1$ to the power of $2$ .

$a^{3} - 3 a^{2} b + 3 \cdot 1 a b^{2} + {(- b)}^{3}$

Multiply $3$ by $1$ .

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

Apply the product rule to $- b$ .

$a^{3} - 3 a^{2} b + 3 a b^{2} + {(- 1)}^{3} b^{3}$

Raise $- 1$ to the power of $3$ .

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