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 $- 5$ .

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

Add $- 15 a$ and $8 a$ .

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