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Factor the Expression Using Distributive Property: 4p + 4q + 80 = 4(p + q + ?)
Mathematics
Grade 7
Question Content
Use the distributive property in reverse (factoring) to complete the statement: 4p + 4q + 80 = 4(p + q + ____)
Correct Answer
20
Detailed Solution Steps
1
Step 1: Recall factoring using the distributive property for multiple terms: ab + ac + ad = a(b + c + d), where a is the GCF of all terms.
2
Step 2: Identify the GCF of 4p, 4q, and 80, which is 4.
3
Step 3: Divide each term by the GCF: 4p÷4 = p, 4q÷4 = q, 80÷4 = 20.
4
Step 4: Fill in the blank with 20, so the factored form is 4(p+q+20).
Knowledge Points Involved
1
Factoring Multiple Terms Using Reverse Distributive Property
The reverse distributive property extends to three or more terms: ab + ac + ad = a(b + c + d). It involves finding the GCF of all terms and factoring it out to simplify the expression.
2
Greatest Common Factor (GCF) of Multiple Terms
The GCF of multiple algebraic terms is the largest number or variable that divides each term evenly. For 4p, 4q, and 80, the GCF is 4, as it divides all three terms without a remainder.
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