Simplify (3a-2)(4a+5)

$(3 a - 2) (4 a + 5)$

Step 1

Expand $(3 a - 2) (4 a + 5)$ using the FOIL Method.

Apply the distributive property.

$3 a (4 a + 5) - 2 (4 a + 5)$

Apply the distributive property.

$3 a (4 a) + 3 a \cdot 5 - 2 (4 a + 5)$

Apply the distributive property.

$3 a (4 a) + 3 a \cdot 5 - 2 (4 a) - 2 \cdot 5$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 4 a \cdot a + 3 a \cdot 5 - 2 (4 a) - 2 \cdot 5$

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

Move $a$ .

$3 \cdot 4 (a \cdot a) + 3 a \cdot 5 - 2 (4 a) - 2 \cdot 5$

Multiply $a$ by $a$ .

$3 \cdot 4 a^{2} + 3 a \cdot 5 - 2 (4 a) - 2 \cdot 5$

Multiply $3$ by $4$ .

$12 a^{2} + 3 a \cdot 5 - 2 (4 a) - 2 \cdot 5$

Multiply $5$ by $3$ .

$12 a^{2} + 15 a - 2 (4 a) - 2 \cdot 5$

Multiply $4$ by $- 2$ .

$12 a^{2} + 15 a - 8 a - 2 \cdot 5$

Multiply $- 2$ by $5$ .

$12 a^{2} + 15 a - 8 a - 10$

Subtract $8 a$ from $15 a$ .

$12 a^{2} + 7 a - 10$