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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $2$ .

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

Multiply $3$ by $1$ .

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

Multiply $2$ by $- 1$ .

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

Multiply $- 1$ by $1$ .

$6 x^{2} + 3 x - 2 x - 1$

Subtract $2 x$ from $3 x$ .

$6 x^{2} + x - 1$