Algebraic Expressions and Identities Worksheets for Class 8 - Free Printable

Sure! Let’s solve each of the 10 problems step by step. The task is to evaluate each algebraic expression for the given value of the variable.

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Problem 1:

Expression: \( 3a^2 - 2a - 15 \) at \( a = 10 \)

Solution:

Substitute \( a = 10 \):

\[
3(10)^2 - 2(10) - 15 = 3(100) - 20 - 15 = 300 - 20 - 15 = 265
\]

✔ Answer: 265

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Problem 2:

Expression: \( \frac{7a^2 - 42a + 28}{7} \) at \( a = -\frac{1}{2} \)

Solution:

First, simplify the expression (optional but helpful):

\[
\frac{7a^2 - 42a + 28}{7} = a^2 - 6a + 4
\]

Now substitute \( a = -\frac{1}{2} \):

\[
\left(-\frac{1}{2}\right)^2 - 6\left(-\frac{1}{2}\right) + 4 = \frac{1}{4} + 3 + 4 = \frac{1}{4} + 7 = \frac{29}{4}
\]

✔ Answer: \( \frac{29}{4} \) or 7.25

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Problem 3:

Expression: \( 12b(2b)^2 \) at \( b = -\frac{3}{4} \)

Solution:

First simplify the expression:

\[
12b \cdot (2b)^2 = 12b \cdot 4b^2 = 48b^3
\]

Now substitute \( b = -\frac{3}{4} \):

\[
48 \cdot \left(-\frac{3}{4}\right)^3 = 48 \cdot \left(-\frac{27}{64}\right) = -\frac{48 \cdot 27}{64}
\]

Simplify:

\[
-\frac{1296}{64} = -\frac{81}{4} \quad \text{(divided numerator and denominator by 16)}
\]

✔ Answer: \( -\frac{81}{4} \) or -20.25

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Problem 4:

Expression: \( 3q + \frac{1}{2} \cdot \frac{2}{3}q \) at \( q = 2 \)

Solution:

Simplify the expression first:

\[
3q + \left(\frac{1}{2} \cdot \frac{2}{3}q\right) = 3q + \frac{1}{3}q = \left(3 + \frac{1}{3}\right)q = \frac{10}{3}q
\]

Now substitute \( q = 2 \):

\[
\frac{10}{3} \cdot 2 = \frac{20}{3}
\]

✔ Answer: \( \frac{20}{3} \) or approximately 6.67

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Problem 5:

Expression: \( c^2 + 7c - 12 \) at \( c = -6 \)

Solution:

Substitute \( c = -6 \):

\[
(-6)^2 + 7(-6) - 12 = 36 - 42 - 12 = -18
\]

✔ Answer: -18

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Problem 6:

Expression: \( 6d^2 - 8d + 10 \) at \( d = -\frac{1}{2} \)

Solution:

Substitute \( d = -\frac{1}{2} \):

\[
6\left(-\frac{1}{2}\right)^2 - 8\left(-\frac{1}{2}\right) + 10 = 6\left(\frac{1}{4}\right) + 4 + 10 = \frac{6}{4} + 14 = \frac{3}{2} + 14 = \frac{31}{2}
\]

✔ Answer: \( \frac{31}{2} \) or 15.5

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Problem 7:

Expression: \( 7y^2 - 2y - 7 \) at \( y = -\frac{1}{7} \)

Solution:

Substitute \( y = -\frac{1}{7} \):

\[
7\left(-\frac{1}{7}\right)^2 - 2\left(-\frac{1}{7}\right) - 7 = 7\left(\frac{1}{49}\right) + \frac{2}{7} - 7 = \frac{7}{49} + \frac{2}{7} - 7
\]

Simplify:

\[
\frac{1}{7} + \frac{2}{7} - 7 = \frac{3}{7} - 7 = -\frac{46}{7}
\]

✔ Answer: \( -\frac{46}{7} \)

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Problem 8:

Expression: \( \frac{8f^2 + 20f - 60}{12} \) at \( f = -20 \)

Solution:

First, plug in \( f = -20 \):

Numerator:

\[
8(-20)^2 + 20(-20) - 60 = 8(400) - 400 - 60 = 3200 - 400 - 60 = 2740
\]

Now divide by 12:

\[
\frac{2740}{12} = \frac{685}{3} \quad \text{(simplified by dividing numerator and denominator by 4)}
\]

✔ Answer: \( \frac{685}{3} \) or approximately 228.33

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Problem 9:

Expression: \( 8m^2 - 3m + 97 \) at \( m = 5 \)

Solution:

Substitute \( m = 5 \):

\[
8(5)^2 - 3(5) + 97 = 8(25) - 15 + 97 = 200 - 15 + 97 = 282
\]

✔ Answer: 282

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Problem 10:

Expression: \( 8k^2 - 12k - 13 \) at \( k = \frac{3}{4} \)

Solution:

Substitute \( k = \frac{3}{4} \):

\[
8\left(\frac{3}{4}\right)^2 - 12\left(\frac{3}{4}\right) - 13 = 8\left(\frac{9}{16}\right) - 9 - 13 = \frac{72}{16} - 22 = \frac{9}{2} - 22
\]

Convert to common denominator:

\[
\frac{9}{2} - \frac{44}{2} = -\frac{35}{2}
\]

✔ Answer: \( -\frac{35}{2} \) or -17.5

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## ✔ Final Answers Summary:

1. 265
2. \( \frac{29}{4} \)
3. \( -\frac{81}{4} \)
4. \( \frac{20}{3} \)
5. -18
6. \( \frac{31}{2} \)
7. \( -\frac{46}{7} \)
8. \( \frac{685}{3} \)
9. 282
10. \( -\frac{35}{2} \)

Let me know if you’d like these shown with work in a printable format or need help understanding any step!