Simplify -2+5(a-2b+1)-3(8-2a+b)

$- 2 + 5 (a - 2 b + 1) - 3 (8 - 2 a + b)$

Step 1

Simplify each term.

Apply the distributive property.

$- 2 + 5 a + 5 (- 2 b) + 5 \cdot 1 - 3 (8 - 2 a + b)$

Simplify.

Multiply $- 2$ by $5$ .

$- 2 + 5 a - 10 b + 5 \cdot 1 - 3 (8 - 2 a + b)$

Multiply $5$ by $1$ .

$- 2 + 5 a - 10 b + 5 - 3 (8 - 2 a + b)$

Apply the distributive property.

$- 2 + 5 a - 10 b + 5 - 3 \cdot 8 - 3 (- 2 a) - 3 b$

Simplify.

Multiply $- 3$ by $8$ .

$- 2 + 5 a - 10 b + 5 - 24 - 3 (- 2 a) - 3 b$

Multiply $- 2$ by $- 3$ .

$- 2 + 5 a - 10 b + 5 - 24 + 6 a - 3 b$

Step 2

Simplify by adding terms.

Add $- 2$ and $5$ .

$5 a - 10 b + 3 - 24 + 6 a - 3 b$

Add $5 a$ and $6 a$ .

$11 a - 10 b + 3 - 24 - 3 b$

Subtract $3 b$ from $- 10 b$ .

$11 a - 13 b + 3 - 24$

Subtract $24$ from $3$ .

$11 a - 13 b - 21$