Expressions - Add and Subtract - Algebraic Expressions worksheet ... - Free Printable

To simplify the given expressions, we need to combine like terms. Like terms are terms that have the same variables raised to the same powers. Let's solve each expression step by step.

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1. \( 4ax - 5ax + 4 \)

- Combine the like terms \( 4ax \) and \( -5ax \):
\[
4ax - 5ax = -ax
\]
- The constant term \( 4 \) remains as it is.
- Simplified expression:
\[
-ax + 4
\]

Answer: \( -ax + 4 \)

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2. \( 12ax^2 - 8ax^2 + 4 \)

- Combine the like terms \( 12ax^2 \) and \( -8ax^2 \):
\[
12ax^2 - 8ax^2 = 4ax^2
\]
- The constant term \( 4 \) remains as it is.
- Simplified expression:
\[
4ax^2 + 4
\]

Answer: \( 4ax^2 + 4 \)

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3. \( 4a^2x - 5a^2x + 4y - 9y \)

- Combine the like terms \( 4a^2x \) and \( -5a^2x \):
\[
4a^2x - 5a^2x = -a^2x
\]
- Combine the like terms \( 4y \) and \( -9y \):
\[
4y - 9y = -5y
\]
- Simplified expression:
\[
-a^2x - 5y
\]

Answer: \( -a^2x - 5y \)

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4. \( -3y^2x + 6xy^2 - 2y - 7y \)

- Note that \( -3y^2x \) and \( 6xy^2 \) are like terms because \( y^2x \) is the same as \( xy^2 \):
\[
-3y^2x + 6xy^2 = 3xy^2
\]
- Combine the like terms \( -2y \) and \( -7y \):
\[
-2y - 7y = -9y
\]
- Simplified expression:
\[
3xy^2 - 9y
\]

Answer: \( 3xy^2 - 9y \)

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5. \( 6m^2n^3 - 12mn - 5mn - 8m^2n^3 \)

- Combine the like terms \( 6m^2n^3 \) and \( -8m^2n^3 \):
\[
6m^2n^3 - 8m^2n^3 = -2m^2n^3
\]
- Combine the like terms \( -12mn \) and \( -5mn \):
\[
-12mn - 5mn = -17mn
\]
- Simplified expression:
\[
-2m^2n^3 - 17mn
\]

Answer: \( -2m^2n^3 - 17mn \)

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6. \( -21mn + 4f - 2f - 5mn \)

- Combine the like terms \( -21mn \) and \( -5mn \):
\[
-21mn - 5mn = -26mn
\]
- Combine the like terms \( 4f \) and \( -2f \):
\[
4f - 2f = 2f
\]
- Simplified expression:
\[
-26mn + 2f
\]

Answer: \( -26mn + 2f \)

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7. \( 7x^2y - xy^2 - 5x^2y - 2xy^2 \)

- Combine the like terms \( 7x^2y \) and \( -5x^2y \):
\[
7x^2y - 5x^2y = 2x^2y
\]
- Combine the like terms \( -xy^2 \) and \( -2xy^2 \):
\[
-xy^2 - 2xy^2 = -3xy^2
\]
- Simplified expression:
\[
2x^2y - 3xy^2
\]

Answer: \( 2x^2y - 3xy^2 \)

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8. \( 3xy + 8yx - 5 + 4 \)

- Note that \( 3xy \) and \( 8yx \) are like terms (since multiplication is commutative):
\[
3xy + 8yx = 11xy
\]
- Combine the constant terms \( -5 \) and \( 4 \):
\[
-5 + 4 = -1
\]
- Simplified expression:
\[
11xy - 1
\]

Answer: \( 11xy - 1 \)

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9. \( 10x - 4 + 5 + x \)

- Combine the like terms \( 10x \) and \( x \):
\[
10x + x = 11x
\]
- Combine the constant terms \( -4 \) and \( 5 \):
\[
-4 + 5 = 1
\]
- Simplified expression:
\[
11x + 1
\]

Answer: \( 11x + 1 \)

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10. \( -3a^2x^2 + 5a^2x^2 + 4y - 3y \)

- Combine the like terms \( -3a^2x^2 \) and \( 5a^2x^2 \):
\[
-3a^2x^2 + 5a^2x^2 = 2a^2x^2
\]
- Combine the like terms \( 4y \) and \( -3y \):
\[
4y - 3y = y
\]
- Simplified expression:
\[
2a^2x^2 + y
\]

Answer: \( 2a^2x^2 + y \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & -ax + 4 \\
2. & 4ax^2 + 4 \\
3. & -a^2x - 5y \\
4. & 3xy^2 - 9y \\
5. & -2m^2n^3 - 17mn \\
6. & -26mn + 2f \\
7. & 2x^2y - 3xy^2 \\
8. & 11xy - 1 \\
9. & 11x + 1 \\
10. & 2a^2x^2 + y \\
\end{array}
}
\]