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Factor the Expression Using Distributive Property: ax + ay = ?(x + y)
Mathematics
Grade 7
Question Content
Use the distributive property in reverse (factoring) to complete the statement: ax + ay = ____(x + y)
Correct Answer
a
Detailed Solution Steps
1
Step 1: Recall factoring using the distributive property: ab + ac = a(b + c), where a is the greatest common factor (GCF) of ab and ac.
2
Step 2: Identify the GCF of ax and ay, which is a.
3
Step 3: Factor out the GCF from both terms, so the factored form is a(x+y).
4
Step 4: Fill in the blank with a.
Knowledge Points Involved
1
Factoring Variable GCFs Using Reverse Distributive Property
When the GCF of algebraic terms is a variable, like a in ax and ay, factoring it out follows the same rule: ax + ay = a(x+y). This is used to simplify expressions with shared variable factors.
2
Greatest Common Factor (GCF) of Variable Terms
The GCF of terms with the same variable is the variable itself, as it divides each term evenly. For ax and ay, the GCF is a, since a divides ax and ay without a remainder.
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