Simplify (2x-1)(6x-7)

$(2 x - 1) (6 x - 7)$

Step 1

Expand $(2 x - 1) (6 x - 7)$ using the FOIL Method.

Apply the distributive property.

$2 x (6 x - 7) - 1 (6 x - 7)$

Apply the distributive property.

$2 x (6 x) + 2 x \cdot - 7 - 1 (6 x - 7)$

Apply the distributive property.

$2 x (6 x) + 2 x \cdot - 7 - 1 (6 x) - 1 \cdot - 7$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 6 x \cdot x + 2 x \cdot - 7 - 1 (6 x) - 1 \cdot - 7$

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

Move $x$ .

$2 \cdot 6 (x \cdot x) + 2 x \cdot - 7 - 1 (6 x) - 1 \cdot - 7$

Multiply $x$ by $x$ .

$2 \cdot 6 x^{2} + 2 x \cdot - 7 - 1 (6 x) - 1 \cdot - 7$

Multiply $2$ by $6$ .

$12 x^{2} + 2 x \cdot - 7 - 1 (6 x) - 1 \cdot - 7$

Multiply $- 7$ by $2$ .

$12 x^{2} - 14 x - 1 (6 x) - 1 \cdot - 7$

Multiply $6$ by $- 1$ .

$12 x^{2} - 14 x - 6 x - 1 \cdot - 7$

Multiply $- 1$ by $- 7$ .

$12 x^{2} - 14 x - 6 x + 7$

Subtract $6 x$ from $- 14 x$ .

$12 x^{2} - 20 x + 7$