Simplify (3xy-1)(4xy+2)

$(3 x y - 1) (4 x y + 2)$

Step 1

Expand $(3 x y - 1) (4 x y + 2)$ using the FOIL Method.

Apply the distributive property.

$3 x y (4 x y + 2) - 1 (4 x y + 2)$

Apply the distributive property.

$3 x y (4 x y) + 3 x y \cdot 2 - 1 (4 x y + 2)$

Apply the distributive property.

$3 x y (4 x y) + 3 x y \cdot 2 - 1 (4 x y) - 1 \cdot 2$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 (x \cdot x) y (4 y) + 3 x y \cdot 2 - 1 (4 x y) - 1 \cdot 2$

Multiply $x$ by $x$ .

$3 x^{2} y (4 y) + 3 x y \cdot 2 - 1 (4 x y) - 1 \cdot 2$

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

Move $y$ .

$3 x^{2} (y \cdot y) \cdot 4 + 3 x y \cdot 2 - 1 (4 x y) - 1 \cdot 2$

Multiply $y$ by $y$ .

$3 x^{2} y^{2} \cdot 4 + 3 x y \cdot 2 - 1 (4 x y) - 1 \cdot 2$

Multiply $4$ by $3$ .

$12 x^{2} y^{2} + 3 x y \cdot 2 - 1 (4 x y) - 1 \cdot 2$

Multiply $2$ by $3$ .

$12 x^{2} y^{2} + 6 x y - 1 (4 x y) - 1 \cdot 2$

Multiply $4$ by $- 1$ .

$12 x^{2} y^{2} + 6 x y - 4 (x y) - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$12 x^{2} y^{2} + 6 x y - 4 x y - 2$

Subtract $4 x y$ from $6 x y$ .

$12 x^{2} y^{2} + 2 x y - 2$