Algebra 2 | AIAN - RM 302 - Free Printable

Problem: Evaluate each expression.

#### Part 1: Evaluate each expression

1. Expression: \( (7 - 2) \div 5 \)
- Simplify inside the parentheses first:
\[
7 - 2 = 5
\]
- Then divide:
\[
5 \div 5 = 1
\]
- Answer: \( \boxed{1} \)

2. Expression: \( (3 + 3)^2 \)
- Simplify inside the parentheses first:
\[
3 + 3 = 6
\]
- Then square the result:
\[
6^2 = 36
\]
- Answer: \( \boxed{36} \)

3. Expression: \( (6 - 3)^2 \)
- Simplify inside the parentheses first:
\[
6 - 3 = 3
\]
- Then square the result:
\[
3^2 = 9
\]
- Answer: \( \boxed{9} \)

4. Expression: \( 5 + (16 + 2) \div 3 \)
- Simplify inside the parentheses first:
\[
16 + 2 = 18
\]
- Then divide:
\[
18 \div 3 = 6
\]
- Finally, add:
\[
5 + 6 = 11
\]
- Answer: \( \boxed{11} \)

5. Expression: \( (-6 \times 2) \div -3 \)
- Multiply inside the parentheses first:
\[
-6 \times 2 = -12
\]
- Then divide:
\[
-12 \div -3 = 4
\]
- Answer: \( \boxed{4} \)

6. Expression: \( 2 + 12 \div 2 + 1 \)
- Perform division first (following the order of operations):
\[
12 \div 2 = 6
\]
- Then add:
\[
2 + 6 + 1 = 9
\]
- Answer: \( \boxed{9} \)

7. Expression: \( -4 - (1 - 5) - (-4)^2 \)
- Simplify inside the parentheses first:
\[
1 - 5 = -4
\]
- Square the term \( -4 \):
\[
(-4)^2 = 16
\]
- Substitute back and simplify:
\[
-4 - (-4) - 16 = -4 + 4 - 16 = 0 - 16 = -16
\]
- Answer: \( \boxed{-16} \)

8. Expression: \( -3 \times 2 \times 2(-3 - 1) \)
- Simplify inside the parentheses first:
\[
-3 - 1 = -4
\]
- Multiply step-by-step:
\[
-3 \times 2 = -6
\]
\[
-6 \times 2 = -12
\]
\[
-12 \times -4 = 48
\]
- Answer: \( \boxed{48} \)

9. Expression: \( (4 - 3)(1 - (3 + 5)) \times 5 \)
- Simplify inside the innermost parentheses first:
\[
3 + 5 = 8
\]
- Then simplify the next set of parentheses:
\[
1 - 8 = -7
\]
- Simplify the outer parentheses:
\[
4 - 3 = 1
\]
- Multiply step-by-step:
\[
1 \times -7 = -7
\]
\[
-7 \times 5 = -35
\]
- Answer: \( \boxed{-35} \)

10. Expression: \( ((-16 - (-2 + 1)) \times 2) \div 5 \)
- Simplify inside the innermost parentheses first:
\[
-2 + 1 = -1
\]
- Then simplify the next set of parentheses:
\[
-16 - (-1) = -16 + 1 = -15
\]
- Multiply:
\[
-15 \times 2 = -30
\]
- Finally, divide:
\[
-30 \div 5 = -6
\]
- Answer: \( \boxed{-6} \)

11. Expression: \( 2 - 8 \div -2 - 3 - 12 \div -6 \times -2 \)
- Perform division and multiplication first (following the order of operations):
\[
8 \div -2 = -4
\]
\[
12 \div -6 = -2
\]
\[
-2 \times -2 = 4
\]
- Substitute back and simplify:
\[
2 - (-4) - 3 - 4 = 2 + 4 - 3 - 4 = 6 - 3 - 4 = 3 - 4 = -1
\]
- Answer: \( \boxed{-1} \)

12. Expression: \( (-11 - 6 - -5 + 1 + 3 \times 2) \div -5 \)
- Perform multiplication first:
\[
3 \times 2 = 6
\]
- Simplify inside the parentheses:
\[
-11 - 6 - -5 + 1 + 6 = -11 - 6 + 5 + 1 + 6
\]
\[
-11 - 6 = -17
\]
\[
-17 + 5 = -12
\]
\[
-12 + 1 = -11
\]
\[
-11 + 6 = -5
\]
- Finally, divide:
\[
-5 \div -5 = 1
\]
- Answer: \( \boxed{1} \)

#### Part 2: Evaluate each using the values given

13. Expression: \( y + z + 2 \); use \( y = -6 \) and \( z = 5 \)
- Substitute the given values:
\[
y + z + 2 = -6 + 5 + 2
\]
- Simplify:
\[
-6 + 5 = -1
\]
\[
-1 + 2 = 1
\]
- Answer: \( \boxed{1} \)

14. Expression: \( p(q \div 3 - p) \); use \( p = -6 \) and \( q = -3 \)
- Substitute the given values:
\[
p(q \div 3 - p) = -6((-3 \div 3) - (-6))
\]
- Simplify inside the parentheses:
\[
-3 \div 3 = -1
\]
\[
-1 - (-6) = -1 + 6 = 5
\]
- Multiply:
\[
-6 \times 5 = -30
\]
- Answer: \( \boxed{-30} \)

Final Answers:

\[
\boxed{1, 36, 9, 11, 4, 9, -16, 48, -35, -6, -1, 1, 1, -30}
\]