Expressions Notes and Worksheets - Lindsay Bowden - Free Printable

Let's solve each problem step by step, following the order on the worksheet.

---

1. Evaluate the expression:

$$
-5 - 2(x + 7) - y \quad \text{when } x = 3 \text{ and } y = -6
$$

Step-by-step:

Substitute $x = 3$, $y = -6$:
$$
-5 - 2(3 + 7) - (-6)
$$

Simplify inside parentheses:
$$
-5 - 2(10) + 6
$$

Multiply:
$$
-5 - 20 + 6
$$

Add:
$$
-19
$$

✔ Answer: $-19$

---

2. Simplify the expression:

$$
5 - 4(x + 2) - 7
$$

Distribute $-4$:
$$
5 - 4x - 8 - 7
$$

Combine like terms:
$$
-4x - 10
$$

✔ Answer: $-4x - 10$

---

3. Simplify the expression:

$$
3 + 2 \cdot 5 - 3(2 + 1)
$$

Order of operations (PEMDAS):

First, parentheses:
$$
3 + 2 \cdot 5 - 3(3)
$$

Then multiplication:
$$
3 + 10 - 9
$$

Now add/subtract left to right:
$$
13 - 9 = 4
$$

✔ Answer: $4$

---

4. Evaluate the expression:

$$
7x^2 - 5y^3 + x \quad \text{when } x = -2, y = 3
$$

Substitute values:

$$
7(-2)^2 - 5(3)^3 + (-2)
$$

Calculate exponents:
$$
7(4) - 5(27) - 2
$$

Multiply:
$$
28 - 135 - 2
$$

Add/subtract:
$$
-109
$$

✔ Answer: $-109$

---

5. Simplify the expression:

$$
2(x + 5) - 4(y - 22)
$$

Distribute:
$$
2x + 10 - 4y + 88
$$

Combine like terms:
$$
2x - 4y + 98
$$

✔ Answer: $2x - 4y + 98$

---

6. Evaluate the expression:

$$
8y^2 - y + 18 \quad \text{when } y = -4
$$

Substitute:
$$
8(-4)^2 - (-4) + 18
$$

Exponent:
$$
8(16) + 4 + 18
$$

Multiply:
$$
128 + 4 + 18 = 150
$$

✔ Answer: $150$

---

7. Evaluate the expression:

$$
3x^2 + 4(y - 6) + x \quad \text{when } x = 2, y = -5
$$

Substitute:
$$
3(2)^2 + 4(-5 - 6) + 2
$$

Exponent:
$$
3(4) + 4(-11) + 2
$$

Multiply:
$$
12 - 44 + 2 = -30
$$

✔ Answer: $-30$

---

8. Simplify the expression:

$$
-4(x - 8) + y + 10
$$

Distribute:
$$
-4x + 32 + y + 10
$$

Combine like terms:
$$
-4x + y + 42
$$

✔ Answer: $-4x + y + 42$

---

9. Simplify the expression:

$$
6x + 2(y + 7) - 22 + 11
$$

Distribute:
$$
6x + 2y + 14 - 22 + 11
$$

Combine constants:
$$
6x + 2y + (14 - 22 + 11) = 6x + 2y + 3
$$

✔ Answer: $6x + 2y + 3$

---

10. Evaluate the expression:

$$
3x^2 - 8(x + 7) + y \quad \text{when } x = 2, y = -7
$$

Substitute:
$$
3(2)^2 - 8(2 + 7) + (-7)
$$

Exponent:
$$
3(4) - 8(9) - 7
$$

Multiply:
$$
12 - 72 - 7 = -67
$$

✔ Answer: $-67$

---

11. Evaluate the expression:

$$
(x^2 + 1) - 5(y - 8) \quad \text{when } x = -2, y = 9
$$

Substitute:
$$
((-2)^2 + 1) - 5(9 - 8)
$$

Exponent:
$$
(4 + 1) - 5(1) = 5 - 5 = 0
$$

✔ Answer: $0$

---

12. Simplify the expression:

$$
-7(x + 4) - 4(y + 5) - 2
$$

Distribute:
$$
-7x - 28 - 4y - 20 - 2
$$

Combine like terms:
$$
-7x - 4y - 50
$$

✔ Answer: $-7x - 4y - 50$

---

✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $-19$ |
| 2 | $-4x - 10$ |
| 3 | $4$ |
| 4 | $-109$ |
| 5 | $2x - 4y + 98$ |
| 6 | $150$ |
| 7 | $-30$ |
| 8 | $-4x + y + 42$ |
| 9 | $6x + 2y + 3$ |
| 10 | $-67$ |
| 11 | $0$ |
| 12 | $-7x - 4y - 50$ |

Let me know if you'd like this formatted for printing or need explanations in a different format!