Simplify 3x(x-1)-4x(3x-2)

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

Step 1

Simplify each term.

Apply the distributive property.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $3$ .

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

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 2$ by $- 4$ .

$3 x^{2} - 3 x - 4 \cdot 3 x \cdot x + 8 x$

Simplify each term.

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

Move $x$ .

$3 x^{2} - 3 x - 4 \cdot 3 (x \cdot x) + 8 x$

Multiply $x$ by $x$ .

$3 x^{2} - 3 x - 4 \cdot 3 x^{2} + 8 x$

Multiply $- 4$ by $3$ .

$3 x^{2} - 3 x - 12 x^{2} + 8 x$

Step 2

Simplify by adding terms.

Subtract $12 x^{2}$ from $3 x^{2}$ .

$- 9 x^{2} - 3 x + 8 x$

Add $- 3 x$ and $8 x$ .

$- 9 x^{2} + 5 x$