Algebra worksheet for evaluating expressions with variables a and b, featuring 18 math problems.

To solve the problem, we need to evaluate each expression given in the worksheet for \( a = -1 \) and \( b = 5 \). Let's go through each expression step by step.

Expression 1: \( 5b - 5 + 10 \)

\[
5b - 5 + 10 = 5(5) - 5 + 10 = 25 - 5 + 10 = 30
\]

Expression 2: \( 2a^2 - 13 + 10 \)

\[
2a^2 - 13 + 10 = 2(-1)^2 - 13 + 10 = 2(1) - 13 + 10 = 2 - 13 + 10 = -1
\]

Expression 3: \( b + b^2 - 5 \)

\[
b + b^2 - 5 = 5 + (5)^2 - 5 = 5 + 25 - 5 = 25
\]

Expression 4: \( 4a - 6 + 2b \)

\[
4a - 6 + 2b = 4(-1) - 6 + 2(5) = -4 - 6 + 10 = 0
\]

Expression 5: \( 2a^2 - 9a + 10 \)

\[
2a^2 - 9a + 10 = 2(-1)^2 - 9(-1) + 10 = 2(1) + 9 + 10 = 2 + 9 + 10 = 21
\]

Expression 6: \( b + 2a^2 - 5 \)

\[
b + 2a^2 - 5 = 5 + 2(-1)^2 - 5 = 5 + 2(1) - 5 = 5 + 2 - 5 = 2
\]

Expression 7: \( 6a^2 + b - 10 \)

\[
6a^2 + b - 10 = 6(-1)^2 + 5 - 10 = 6(1) + 5 - 10 = 6 + 5 - 10 = 1
\]

Expression 8: \( 10 + b^2 - 2b^2 \)

\[
10 + b^2 - 2b^2 = 10 + (5)^2 - 2(5)^2 = 10 + 25 - 50 = -15
\]

Expression 9: \( 3a + 2b + 5 \)

\[
3a + 2b + 5 = 3(-1) + 2(5) + 5 = -3 + 10 + 5 = 12
\]

Expression 10: \( a + 3b - 15 \)

\[
a + 3b - 15 = -1 + 3(5) - 15 = -1 + 15 - 15 = -1
\]

Expression 11: \( 3a^2 + b^2 - 28 \)

\[
3a^2 + b^2 - 28 = 3(-1)^2 + (5)^2 - 28 = 3(1) + 25 - 28 = 3 + 25 - 28 = 0
\]

Expression 12: \( -5a - 2b + 15 \)

\[
-5a - 2b + 15 = -5(-1) - 2(5) + 15 = 5 - 10 + 15 = 10
\]

Expression 13: \( a + 2a^2 - 3 \)

\[
a + 2a^2 - 3 = -1 + 2(-1)^2 - 3 = -1 + 2(1) - 3 = -1 + 2 - 3 = -2
\]

Expression 14: \( 9a^2 - 4 + b \)

\[
9a^2 - 4 + b = 9(-1)^2 - 4 + 5 = 9(1) - 4 + 5 = 9 - 4 + 5 = 10
\]

Expression 15: \( 6 + 16a^2 - a^2 \)

\[
6 + 16a^2 - a^2 = 6 + 16(-1)^2 - (-1)^2 = 6 + 16(1) - 1 = 6 + 16 - 1 = 21
\]

Expression 16: \( -10 + 5b - b^2 \)

\[
-10 + 5b - b^2 = -10 + 5(5) - (5)^2 = -10 + 25 - 25 = -10
\]

Expression 17: \( 2a + 3 + a^2 \)

\[
2a + 3 + a^2 = 2(-1) + 3 + (-1)^2 = -2 + 3 + 1 = 2
\]

Expression 18: \( 15 + a^2 - b^2 \)

\[
15 + a^2 - b^2 = 15 + (-1)^2 - (5)^2 = 15 + 1 - 25 = -9
\]

Expression 19: \( 3b^2 + a + 45 \)

\[
3b^2 + a + 45 = 3(5)^2 + (-1) + 45 = 3(25) - 1 + 45 = 75 - 1 + 45 = 119
\]

Expression 20: \( 3a + b^2 - 12 \)

\[
3a + b^2 - 12 = 3(-1) + (5)^2 - 12 = -3 + 25 - 12 = 10
\]

Expression 21: \( 2 - 2a^2 - 4b \)

\[
2 - 2a^2 - 4b = 2 - 2(-1)^2 - 4(5) = 2 - 2(1) - 20 = 2 - 2 - 20 = -20
\]

Final Answer:

\[
\boxed{
\begin{array}{ccc}
30 & -1 & 25 \\
0 & 21 & 2 \\
1 & -15 & 12 \\
-1 & 0 & 10 \\
-2 & 10 & 21 \\
-10 & 2 & -9 \\
119 & 10 & -20 \\
\end{array}
}
\]