Simplify (x-2)(3x-4)

$(x - 2) (3 x - 4)$

Step 1

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

Apply the distributive property.

$x (3 x - 4) - 2 (3 x - 4)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $- 4$ to the left of $x$ .

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

Multiply $3$ by $- 2$ .

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

Multiply $- 2$ by $- 4$ .

$3 x^{2} - 4 x - 6 x + 8$

Subtract $6 x$ from $- 4 x$ .

$3 x^{2} - 10 x + 8$