Math worksheet for evaluating algebraic expressions with variables.

To solve the given algebraic expressions, we will substitute the provided values for each variable and simplify step by step. Let's go through each section:

---

Section 1: Evaluate the following expressions for \( x = 4 \)

1. \( x + 8 \)
\[
x + 8 = 4 + 8 = 12
\]

2. \( 2x - 1 \)
\[
2x - 1 = 2(4) - 1 = 8 - 1 = 7
\]

3. \( 10 + x^2 \)
\[
10 + x^2 = 10 + 4^2 = 10 + 16 = 26
\]

4. \( -x - 12 \)
\[
-x - 12 = -(4) - 12 = -4 - 12 = -16
\]

5. \( -4 + x^2 \)
\[
-4 + x^2 = -4 + 4^2 = -4 + 16 = 12
\]

6. \( x^2 - 1 \)
\[
x^2 - 1 = 4^2 - 1 = 16 - 1 = 15
\]

---

Section 2: Evaluate the following expressions for \( y = -2 \)

1. \( 3y - 3 \)
\[
3y - 3 = 3(-2) - 3 = -6 - 3 = -9
\]

2. \( -2y - 16 \)
\[
-2y - 16 = -2(-2) - 16 = 4 - 16 = -12
\]

3. \( 16 + y^2 \)
\[
16 + y^2 = 16 + (-2)^2 = 16 + 4 = 20
\]

4. \( -2y + 20 \)
\[
-2y + 20 = -2(-2) + 20 = 4 + 20 = 24
\]

5. \( y^2 + 12 \)
\[
y^2 + 12 = (-2)^2 + 12 = 4 + 12 = 16
\]

6. \( -y^2 - 20 \)
\[
-y^2 - 20 = -(-2)^2 - 20 = -4 - 20 = -24
\]

---

Section 3: Evaluate the following expressions for \( t = -5 \)

1. \( t^2 + 75 \)
\[
t^2 + 75 = (-5)^2 + 75 = 25 + 75 = 100
\]

2. \( -t - 25 \)
\[
-t - 25 = -(-5) - 25 = 5 - 25 = -20
\]

3. \( -t + 10 \)
\[
-t + 10 = -(-5) + 10 = 5 + 10 = 15
\]

4. \( 22 - 2t \)
\[
22 - 2t = 22 - 2(-5) = 22 + 10 = 32
\]

5. \( -4t - 5 \)
\[
-4t - 5 = -4(-5) - 5 = 20 - 5 = 15
\]

6. \( -t - 10 \)
\[
-t - 10 = -(-5) - 10 = 5 - 10 = -5
\]

---

Section 4: Evaluate the following expressions for \( q = -1 \)

1. \( 12 + q^2 \)
\[
12 + q^2 = 12 + (-1)^2 = 12 + 1 = 13
\]

2. \( -q^2 - q \)
\[
-q^2 - q = -(-1)^2 - (-1) = -1 + 1 = 0
\]

3. \( q + 2q \)
\[
q + 2q = -1 + 2(-1) = -1 - 2 = -3
\]

4. \( -2q - 30 \)
\[
-2q - 30 = -2(-1) - 30 = 2 - 30 = -28
\]

5. \( -q - 2q \)
\[
-q - 2q = -(-1) - 2(-1) = 1 + 2 = 3
\]

6. \( 3q^2 - 3 \)
\[
3q^2 - 3 = 3(-1)^2 - 3 = 3(1) - 3 = 3 - 3 = 0
\]

---

Section 5: Evaluate the following expressions for \( s = -3 \)

1. \( s^2 \)
\[
s^2 = (-3)^2 = 9
\]

2. \( 2s - 1 \)
\[
2s - 1 = 2(-3) - 1 = -6 - 1 = -7
\]

3. \( s + s^3 \)
\[
s + s^3 = -3 + (-3)^3 = -3 + (-27) = -3 - 27 = -30
\]

4. \( s + (-1) \)
\[
s + (-1) = -3 + (-1) = -3 - 1 = -4
\]

5. \( -s + 27 \)
\[
-s + 27 = -(-3) + 27 = 3 + 27 = 30
\]

6. \( s^2 - 1 \)
\[
s^2 - 1 = (-3)^2 - 1 = 9 - 1 = 8
\]

---

Final Answers

1. For \( x = 4 \):
\[
\boxed{12, 7, 26, -16, 12, 15}
\]

2. For \( y = -2 \):
\[
\boxed{-9, -12, 20, 24, 16, -24}
\]

3. For \( t = -5 \):
\[
\boxed{100, -20, 15, 32, 15, -5}
\]

4. For \( q = -1 \):
\[
\boxed{13, 0, -3, -28, 3, 0}
\]

5. For \( s = -3 \):
\[
\boxed{9, -7, -30, -4, 30, 8}
\]