Simplify -2(3a+2b-1)+3(a+4b-2)

$- 2 (3 a + 2 b - 1) + 3 (a + 4 b - 2)$

Step 1

Simplify each term.

Apply the distributive property.

$- 2 (3 a) - 2 (2 b) - 2 \cdot - 1 + 3 (a + 4 b - 2)$

Simplify.

Multiply $3$ by $- 2$ .

$- 6 a - 2 (2 b) - 2 \cdot - 1 + 3 (a + 4 b - 2)$

Multiply $2$ by $- 2$ .

$- 6 a - 4 b - 2 \cdot - 1 + 3 (a + 4 b - 2)$

Multiply $- 2$ by $- 1$ .

$- 6 a - 4 b + 2 + 3 (a + 4 b - 2)$

Apply the distributive property.

$- 6 a - 4 b + 2 + 3 a + 3 (4 b) + 3 \cdot - 2$

Simplify.

Multiply $4$ by $3$ .

$- 6 a - 4 b + 2 + 3 a + 12 b + 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$- 6 a - 4 b + 2 + 3 a + 12 b - 6$

Step 2

Simplify by adding terms.

Add $- 6 a$ and $3 a$ .

$- 3 a - 4 b + 2 + 12 b - 6$

Add $- 4 b$ and $12 b$ .

$- 3 a + 8 b + 2 - 6$

Subtract $6$ from $2$ .

$- 3 a + 8 b - 4$