Find the Product (2a-3b)(4a+5.5b+2.8)

$(2 a - 3 b) (4 a + 5.5 b + 2.8)$

Expand $(2 a - 3 b) (4 a + 5.5 b + 2.8)$ by multiplying each term in the first expression by each term in the second expression.

$2 a (4 a) + 2 a (5.5 b) + 2 a \cdot 2.8 - 3 b (4 a) - 3 b (5.5 b) - 3 b \cdot 2.8$

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 4 a \cdot a + 2 a (5.5 b) + 2 a \cdot 2.8 - 3 b (4 a) - 3 b (5.5 b) - 3 b \cdot 2.8$

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

Move $a$ .

$2 \cdot 4 (a \cdot a) + 2 a (5.5 b) + 2 a \cdot 2.8 - 3 b (4 a) - 3 b (5.5 b) - 3 b \cdot 2.8$

Multiply $a$ by $a$ .

$2 \cdot 4 a^{2} + 2 a (5.5 b) + 2 a \cdot 2.8 - 3 b (4 a) - 3 b (5.5 b) - 3 b \cdot 2.8$

Multiply $2$ by $4$ .

$8 a^{2} + 2 a (5.5 b) + 2 a \cdot 2.8 - 3 b (4 a) - 3 b (5.5 b) - 3 b \cdot 2.8$

Rewrite using the commutative property of multiplication.

$8 a^{2} + 2 \cdot 5.5 a b + 2 a \cdot 2.8 - 3 b (4 a) - 3 b (5.5 b) - 3 b \cdot 2.8$

Multiply $2$ by $5.5$ .

$8 a^{2} + 11 a b + 2 a \cdot 2.8 - 3 b (4 a) - 3 b (5.5 b) - 3 b \cdot 2.8$

Multiply $2.8$ by $2$ .

$8 a^{2} + 11 a b + 5.6 a - 3 b (4 a) - 3 b (5.5 b) - 3 b \cdot 2.8$

Rewrite using the commutative property of multiplication.

$8 a^{2} + 11 a b + 5.6 a - 3 \cdot 4 b a - 3 b (5.5 b) - 3 b \cdot 2.8$

Multiply $- 3$ by $4$ .

$8 a^{2} + 11 a b + 5.6 a - 12 b a - 3 b (5.5 b) - 3 b \cdot 2.8$

Rewrite using the commutative property of multiplication.

$8 a^{2} + 11 a b + 5.6 a - 12 b a - 3 \cdot 5.5 b \cdot b - 3 b \cdot 2.8$

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

Move $b$ .

$8 a^{2} + 11 a b + 5.6 a - 12 b a - 3 \cdot 5.5 (b \cdot b) - 3 b \cdot 2.8$

Multiply $b$ by $b$ .

$8 a^{2} + 11 a b + 5.6 a - 12 b a - 3 \cdot 5.5 b^{2} - 3 b \cdot 2.8$

Multiply $- 3$ by $5.5$ .

$8 a^{2} + 11 a b + 5.6 a - 12 b a - 16.5 b^{2} - 3 b \cdot 2.8$

Multiply $2.8$ by $- 3$ .

$8 a^{2} + 11 a b + 5.6 a - 12 b a - 16.5 b^{2} - 8.4 b$

Subtract $12 b a$ from $11 a b$ .

Move $b$ .

$8 a^{2} + 5.6 a + 11 a b - 12 a b - 16.5 b^{2} - 8.4 b$

Subtract $12 a b$ from $11 a b$ .

$8 a^{2} + 5.6 a - 1 a b - 16.5 b^{2} - 8.4 b$