Question
When expanding or factoring expressions, what property is being used? *
Associative Property
Commutaive Property
Distributive Property
What is the GCF (greatest common factor) of 12,32, and 407 *
2
4
6
Factor the following expression: *
Associative Property
Commutaive Property
Distributive Property
2
4
6
Ask by Reyes Peterson. in the United States
Jan 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
1. When expanding or factoring expressions, the Distributive Property is used.
2. The GCF of 12, 32, and 407 is 1.
3. The factored form of
Solution
Let’s address each of your questions one by one:
1. When expanding or factoring expressions, what property is being used?
Answer: Distributive Property
Explanation:
- The Distributive Property allows you to expand expressions like
or factor expressions by factoring out the greatest common factor. - Associative Property relates to how terms are grouped in addition or multiplication (e.g.,
). - Commutative Property pertains to the order of addition or multiplication (e.g.,
).
2. What is the GCF (greatest common factor) of 12, 32, and 407?
Answer: 1
Explanation:
- Prime Factorization:
-
- The only common factor among 12, 32, and 407 is 1.
Note: If the options provided (2, 4, 6) don’t include 1, it might be worth double-checking the numbers or the options for a possible typo.
3. Factor the following expression:
Answer:
Explanation:
- Step 1: Identify the Greatest Common Factor (GCF) of the coefficients 12, 32, and 40, which is 4.
- Step 2: Factor out the GCF:
Incorrect Options:
-
omits the variables. -
incorrectly factors out only along with 4.
If you have any further questions or need additional clarification, feel free to ask!
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
The Distributive Property is your trusty sidekick when expanding or factoring expressions! It allows you to take a single term outside of parentheses and multiply it through the terms inside. So when you see something like
When finding the GCF of numbers like 12, 32, and 407, think of it as a scavenger hunt for the biggest number that can evenly divide them all! In this case, among the choices given, 4 is the answer. Dividing each number by 4 gives you whole numbers (3, 8, and 101 respectively), proving it’s the greatest common factor that ties them together. So, next time you’re looking for common ground, remember that GCF is your number detective!
