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Factor the Expression Using Distributive Property: 2d + 12 = 2(? + 6)
Mathematics
Grade 7
Question Content
Use the distributive property in reverse (factoring) to complete the statement: 2d + 12 = 2(____ + 6)
Correct Answer
d
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 2d and 12, which is 2.
3
Step 3: Divide each term by the GCF: 2d÷2 = d, 12÷2 = 6.
4
Step 4: Fill in the blank with d, so the factored form is 2(d+6).
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 Mixed Algebraic Terms
The GCF of a term with a variable and a constant is the largest number that divides both the coefficient of the variable term and the constant. For 2d and 12, the GCF is 2, as 2 divides 2 and 12 evenly.
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