Simplify (3y+4)(2y-3)

$(3 y + 4) (2 y - 3)$

Step 1

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

Apply the distributive property.

$3 y (2 y - 3) + 4 (2 y - 3)$

Apply the distributive property.

$3 y (2 y) + 3 y \cdot - 3 + 4 (2 y - 3)$

Apply the distributive property.

$3 y (2 y) + 3 y \cdot - 3 + 4 (2 y) + 4 \cdot - 3$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 2 y \cdot y + 3 y \cdot - 3 + 4 (2 y) + 4 \cdot - 3$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$3 \cdot 2 (y \cdot y) + 3 y \cdot - 3 + 4 (2 y) + 4 \cdot - 3$

Multiply $y$ by $y$ .

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

Multiply $3$ by $2$ .

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

Multiply $- 3$ by $3$ .

$6 y^{2} - 9 y + 4 (2 y) + 4 \cdot - 3$

Multiply $2$ by $4$ .

$6 y^{2} - 9 y + 8 y + 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$6 y^{2} - 9 y + 8 y - 12$

Add $- 9 y$ and $8 y$ .

$6 y^{2} - y - 12$