Simplify (a-b)(a^2+ab+b^2)

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

Step 1

Expand $(a - b) (a^{2} + a b + b^{2})$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a$ .

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

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

Move $b$ .

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

Multiply $b$ by $b$ .

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

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

Move $b^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Combine the opposite terms in $a^{3} + a^{2} b + a b^{2} - b a^{2} - b^{2} a - b^{3}$ .

Reorder the factors in the terms $a^{2} b$ and $- b a^{2}$ .

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

Subtract $a^{2} b$ from $a^{2} b$ .

$a^{3} + a b^{2} + 0 - b^{2} a - b^{3}$

Add $a^{3} + a b^{2}$ and $0$ .

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

Reorder the factors in the terms $a b^{2}$ and $- b^{2} a$ .

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

Subtract $b^{2} a$ from $b^{2} a$ .

$a^{3} + 0 - b^{3}$

Add $a^{3}$ and $0$ .

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

Simplify (a-b)(a^2+ab+b^2)

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