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Factor the Expression Using Distributive Property: 8a + 8b = ?(a + b)
Mathematics
Grade 7
Question Content
Use the distributive property in reverse (factoring) to complete the statement: 8a + 8b = ____(a + b)
Correct Answer
8
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 8a and 8b, which is 8.
3
Step 3: Factor out the GCF from both terms, so the factored form is 8(a+b).
4
Step 4: Fill in the blank with 8.
Knowledge Points Involved
1
Factoring Using the Distributive Property (Reverse Distribution)
Factoring is the reverse of expanding with the distributive property: ab + ac = a(b + c). It involves identifying the greatest common factor (GCF) of the terms and factoring it out of the expression, used to simplify algebraic expressions.
2
Greatest Common Factor (GCF) of Algebraic Terms
The GCF of two algebraic terms is the largest number or variable that divides both terms evenly. For 8a and 8b, the GCF is 8, as it divides both 8a and 8b without a remainder.
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