Simplify (a-b)(a^2-5ab+2)

$(a - b) (a^{2} - 5 a b + 2)$

Expand $(a - b) (a^{2} - 5 a b + 2)$ by multiplying each term in the first expression by each term in the second expression.

$a \cdot a^{2} + a (- 5 a b) + a \cdot 2 - b a^{2} - b (- 5 a b) - b \cdot 2$

Simplify each term.

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

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

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

$a^{1} a^{2} + a (- 5 a b) + a \cdot 2 - b a^{2} - b (- 5 a b) - b \cdot 2$

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

$a^{1 + 2} + a (- 5 a b) + a \cdot 2 - b a^{2} - b (- 5 a b) - b \cdot 2$

Add $1$ and $2$ .

$a^{3} + a (- 5 a b) + a \cdot 2 - b a^{2} - b (- 5 a b) - b \cdot 2$

Rewrite using the commutative property of multiplication.

$a^{3} - 5 a (a b) + a \cdot 2 - b a^{2} - b (- 5 a b) - b \cdot 2$

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

Move $a$ .

$a^{3} - 5 (a \cdot a) b + a \cdot 2 - b a^{2} - b (- 5 a b) - b \cdot 2$

Multiply $a$ by $a$ .

$a^{3} - 5 a^{2} b + a \cdot 2 - b a^{2} - b (- 5 a b) - b \cdot 2$

Move $2$ to the left of $a$ .

$a^{3} - 5 a^{2} b + 2 \cdot a - b a^{2} - b (- 5 a b) - b \cdot 2$

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

Move $b$ .

$a^{3} - 5 a^{2} b + 2 a - b a^{2} - (b \cdot b) (- 5 a) - b \cdot 2$

Multiply $b$ by $b$ .

$a^{3} - 5 a^{2} b + 2 a - b a^{2} - b^{2} (- 5 a) - b \cdot 2$

Rewrite using the commutative property of multiplication.

$a^{3} - 5 a^{2} b + 2 a - b a^{2} - 1 \cdot - 5 b^{2} a - b \cdot 2$

Multiply $- 1$ by $- 5$ .

$a^{3} - 5 a^{2} b + 2 a - b a^{2} + 5 b^{2} a - b \cdot 2$

Multiply $2$ by $- 1$ .

$a^{3} - 5 a^{2} b + 2 a - b a^{2} + 5 b^{2} a - 2 b$

Subtract $b a^{2}$ from $- 5 a^{2} b$ .

Move $b$ .

$a^{3} + 2 a - 5 a^{2} b - 1 a^{2} b + 5 b^{2} a - 2 b$

Subtract $a^{2} b$ from $- 5 a^{2} b$ .

$a^{3} + 2 a - 6 a^{2} b + 5 b^{2} a - 2 b$

Move $b^{2}$ .

$a^{3} + 2 a - 6 a^{2} b + 5 a b^{2} - 2 b$

Move $2 a$ .

$a^{3} - 6 a^{2} b + 5 a b^{2} - 2 b + 2 a$

Move $a^{3}$ .

$- 6 a^{2} b + 5 a b^{2} + a^{3} - 2 b + 2 a$

Reorder $- 6 a^{2} b$ and $5 a b^{2}$ .

$5 a b^{2} - 6 a^{2} b + a^{3} - 2 b + 2 a$