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Factor the Expression Using Distributive Property: nt + 4n = nt(? + ?)
Mathematics
Grade 7
Question Content
Use the distributive property in reverse (factoring) to complete the statement: nt + 4n = nt(____ + ____)
Correct Answer
1, 4/t
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 nt and 4n, which is n. However, the given factored form starts with nt, so divide each term by nt: nt÷nt = 1, 4n÷nt = 4/t.
3
Step 3: Fill in the blanks with 1 and 4/t, so the factored form is nt(1 + 4/t).
Knowledge Points Involved
1
Factoring with Non-GCF Terms
While factoring usually uses the GCF, you can factor out any common term (not just the greatest) by dividing each term by the chosen factor. Here, factoring out nt instead of the GCF n results in a fractional term 4/t.
2
Dividing Algebraic Terms with Variables
When dividing algebraic terms, cancel out common factors in the numerator and denominator. For 4n÷nt, cancel the common n term, leaving 4/t.
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