Expand the Trigonometric Expression (3a+b)(2a-4b)

$(3 a + b) (2 a - 4 b)$

Step 1

Expand $(3 a + b) (2 a - 4 b)$ using the FOIL Method.

Apply the distributive property.

$3 a (2 a - 4 b) + b (2 a - 4 b)$

Apply the distributive property.

$3 a (2 a) + 3 a (- 4 b) + b (2 a - 4 b)$

Apply the distributive property.

$3 a (2 a) + 3 a (- 4 b) + b (2 a) + b (- 4 b)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 2 a \cdot a + 3 a (- 4 b) + b (2 a) + b (- 4 b)$

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

Move $a$ .

$3 \cdot 2 (a \cdot a) + 3 a (- 4 b) + b (2 a) + b (- 4 b)$

Multiply $a$ by $a$ .

$3 \cdot 2 a^{2} + 3 a (- 4 b) + b (2 a) + b (- 4 b)$

Multiply $3$ by $2$ .

$6 a^{2} + 3 a (- 4 b) + b (2 a) + b (- 4 b)$

Rewrite using the commutative property of multiplication.

$6 a^{2} + 3 \cdot - 4 a b + b (2 a) + b (- 4 b)$

Multiply $3$ by $- 4$ .

$6 a^{2} - 12 a b + b (2 a) + b (- 4 b)$

Rewrite using the commutative property of multiplication.

$6 a^{2} - 12 a b + 2 b a + b (- 4 b)$

Rewrite using the commutative property of multiplication.

$6 a^{2} - 12 a b + 2 b a - 4 b \cdot b$

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

Move $b$ .

$6 a^{2} - 12 a b + 2 b a - 4 (b \cdot b)$

Multiply $b$ by $b$ .

$6 a^{2} - 12 a b + 2 b a - 4 b^{2}$

Add $- 12 a b$ and $2 b a$ .

Move $b$ .

$6 a^{2} - 12 a b + 2 a b - 4 b^{2}$

Add $- 12 a b$ and $2 a b$ .

$6 a^{2} - 10 a b - 4 b^{2}$