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Factor the Expression Using Distributive Property: 7x + 7y = 7(x + ?)
Mathematics
Grade 7
Question Content
Use the distributive property in reverse (factoring) to complete the statement: 7x + 7y = 7(x + ____)
Correct Answer
y
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 7x and 7y, which is 7.
3
Step 3: Divide each term by the GCF: 7x÷7 = x, 7y÷7 = y.
4
Step 4: Fill in the blank with y, so the factored form is 7(x+y).
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 7x and 7y, the GCF is 7, as it divides both 7x and 7y without a remainder.
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