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Factor the Expression Using Distributive Property: 5e + 35 = 5(e + ?)
Mathematics
Grade 7
Question Content
Use the distributive property in reverse (factoring) to complete the statement: 5e + 35 = 5(e + ____)
Correct Answer
7
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 5e and 35, which is 5.
3
Step 3: Divide each term by the GCF: 5e÷5 = e, 35÷5 = 7.
4
Step 4: Fill in the blank with 7, so the factored form is 5(e+7).
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 5e and 35, the GCF is 5, as 5 divides 5 and 35 evenly.
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