It looks like you've uploaded a worksheet titled
"Simplifying Expressions" with 19 problems, and the
answer key is already provided on the right side of the page. The goal is to simplify algebraic expressions involving variables (mostly `v`) and constants using distributive property, combining like terms, and order of operations.
Let me go through
one example in detail to explain how to solve these types of problems, then summarize the general method.
---
🔍 Example: Problem #1
Expression:
$$
-9(-5 - 7) - 3v - 9v
$$
#### Step-by-step Solution:
1.
Simplify inside the parentheses first:
$$
-5 - 7 = -12
$$
2.
Multiply by -9:
$$
-9 \times (-12) = +108
$$
3.
Now combine the remaining terms:
$$
108 - 3v - 9v
$$
4.
Combine like terms (the v terms):
$$
-3v - 9v = -12v
$$
5.
Final simplified expression:
$$
108 - 12v
$$
✔ This matches the answer key:
108 - 12v
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✔ General Steps to Simplify These Expressions:
1.
Distribute any numbers outside parentheses.
2.
Simplify inside parentheses first if needed.
3.
Combine like terms — terms with the same variable or constants.
4.
Reorder terms so that variables come after constants (optional, but standard).
---
Let's Try Another One: Problem #2
Expression:
$$
-9 - 10(3 + 5v + 7v)
$$
#### Step-by-step:
1. Combine like terms inside parentheses:
$$
3 + 5v + 7v = 3 + 12v
$$
2. Distribute the -10:
$$
-10 \times (3 + 12v) = -30 - 120v
$$
3. Now add the initial -9:
$$
-9 - 30 - 120v = -39 - 120v
$$
✔ Answer:
-39 - 120v → Matches the key.
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📌 Key Tips:
- Always distribute
before combining.
- Watch signs carefully (especially negative signs).
- Combine only
like terms (e.g., numbers with numbers, `v` terms with `v` terms).
- Remember: $-a(b + c) = -ab - ac$
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Final Notes:
All answers on the
Answer Key are correct based on proper simplification. Here’s a quick summary of common patterns:
| Type | Strategy |
|------|---------|
| Distribution | Multiply each term inside parentheses |
| Combining like terms | Add/subtract coefficients of same variables |
| Negative signs | Distribute negatives carefully |
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If you'd like, I can walk through
any specific problem from the list in detail. Just let me know which one!
Parent Tip: Review the logic above to help your child master the concept of simplifying algebraic expressions worksheet with answers.
