Simplify (3a-8b)(2a-b)

$(3 a - 8 b) (2 a - b)$

Step 1

Expand $(3 a - 8 b) (2 a - b)$ using the FOIL Method.

Apply the distributive property.

$3 a (2 a - b) - 8 b (2 a - b)$

Apply the distributive property.

$3 a (2 a) + 3 a (- b) - 8 b (2 a - b)$

Apply the distributive property.

$3 a (2 a) + 3 a (- b) - 8 b (2 a) - 8 b (- b)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 2 a \cdot a + 3 a (- b) - 8 b (2 a) - 8 b (- b)$

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

Move $a$ .

$3 \cdot 2 (a \cdot a) + 3 a (- b) - 8 b (2 a) - 8 b (- b)$

Multiply $a$ by $a$ .

$3 \cdot 2 a^{2} + 3 a (- b) - 8 b (2 a) - 8 b (- b)$

Multiply $3$ by $2$ .

$6 a^{2} + 3 a (- b) - 8 b (2 a) - 8 b (- b)$

Rewrite using the commutative property of multiplication.

$6 a^{2} + 3 \cdot - 1 a b - 8 b (2 a) - 8 b (- b)$

Multiply $3$ by $- 1$ .

$6 a^{2} - 3 a b - 8 b (2 a) - 8 b (- b)$

Rewrite using the commutative property of multiplication.

$6 a^{2} - 3 a b - 8 \cdot 2 b a - 8 b (- b)$

Multiply $- 8$ by $2$ .

$6 a^{2} - 3 a b - 16 b a - 8 b (- b)$

Rewrite using the commutative property of multiplication.

$6 a^{2} - 3 a b - 16 b a - 8 \cdot - 1 b \cdot b$

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

Move $b$ .

$6 a^{2} - 3 a b - 16 b a - 8 \cdot - 1 (b \cdot b)$

Multiply $b$ by $b$ .

$6 a^{2} - 3 a b - 16 b a - 8 \cdot - 1 b^{2}$

Multiply $- 8$ by $- 1$ .

$6 a^{2} - 3 a b - 16 b a + 8 b^{2}$

Subtract $16 b a$ from $- 3 a b$ .

Move $b$ .

$6 a^{2} - 3 a b - 16 a b + 8 b^{2}$

Subtract $16 a b$ from $- 3 a b$ .

$6 a^{2} - 19 a b + 8 b^{2}$