Simplify (2x-1)(3x+2)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $3$ .

$6 x^{2} + 2 x \cdot 2 - 1 (3 x) - 1 \cdot 2$

Multiply $2$ by $2$ .

$6 x^{2} + 4 x - 1 (3 x) - 1 \cdot 2$

Multiply $3$ by $- 1$ .

$6 x^{2} + 4 x - 3 x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$6 x^{2} + 4 x - 3 x - 2$

Subtract $3 x$ from $4 x$ .

$6 x^{2} + x - 2$