It looks like you've uploaded an image of a
completed worksheet titled *"Simplifying Expressions Sheet 6:1 Answers"*, which shows the
simplified forms of algebraic expressions. The task was to
combine like terms in each expression.
Since this is already a solution sheet (with answers provided), I'll explain
how to solve one or two of these problems step-by-step, so you understand the method behind simplifying algebraic expressions by combining like terms.
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🔍 What are "like terms"?
Like terms are terms that have the
same variable raised to the same power. For example:
- $ 3x $ and $ 5x $ are like terms.
- $ 4y^2 $ and $ -2y^2 $ are like terms.
- Constants (numbers without variables) are also like terms.
You can combine like terms by adding or subtracting their coefficients.
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✔ Example 1: Problem #1
Expression:
$$
7a + 4 + 8
$$
Step-by-step:
1. Identify like terms:
- $ 7a $ → only term with variable $ a $
- $ 4 $ and $ 8 $ → both constants
2. Combine constants:
$$
4 + 8 = 12
$$
3. Write simplified expression:
$$
7a + 12
$$
✔ Answer: $ \boxed{7a + 12} $
---
✔ Example 2: Problem #2
Expression:
$$
b + 5 + b + b
$$
Step-by-step:
1. Group like terms:
- $ b + b + b = 3b $
- Constant: $ 5 $
2. Combine:
$$
3b + 5
$$
✔ Answer: $ \boxed{3b + 5} $
---
✔ Example 3: Problem #15
Expression:
$$
4q - (2 + q)
$$
Step-by-step:
1. Distribute the negative sign across the parentheses:
$$
4q - 2 - q
$$
2. Combine like terms:
- $ 4q - q = 3q $
- Constant: $ -2 $
3. Result:
$$
3q - 2
$$
✔ Answer: $ \boxed{3q - 2} $
---
✔ Example 4: Problem #20
Expression:
$$
2v + 8w - (4w + 5v)
$$
Step-by-step:
1. Distribute the negative sign:
$$
2v + 8w - 4w - 5v
$$
2. Group like terms:
- $ 2v - 5v = -3v $
- $ 8w - 4w = 4w $
3. Final simplified form:
$$
4w - 3v
$$
✔ Answer: $ \boxed{4w - 3v} $
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🧠 General Steps for Simplifying Expressions:
1.
Remove parentheses using distribution (especially if there's a minus sign).
2.
Group like terms (same variables and powers).
3.
Add or subtract coefficients of like terms.
4.
Write the final simplified expression.
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✔ Summary
All the answers on the sheet are correct based on proper combination of like terms. Here’s how you’d approach any similar problem:
>
Example: $ 3x + 2y - x + 4 $
>
> Step 1: $ 3x - x = 2x $
> Step 2: $ 2y $ stays
> Step 3: $ +4 $ stays
> Final: $ 2x + 2y + 4 $
---
Let me know if you'd like help creating your own practice problems or want to go through more examples!
Parent Tip: Review the logic above to help your child master the concept of simplifying algebraic expressions worksheet 7th grade.
