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Factor the Expression Using Distributive Property: kw + wy + w² = w(k + y + ?)
Mathematics
Grade 7
Question Content
Use the distributive property in reverse (factoring) to complete the statement: kw + wy + w² = w(k + y + ____)
Correct Answer
w
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 kw, wy, and w², which is w.
3
Step 3: Divide each term by the GCF: kw÷w = k, wy÷w = y, w²÷w = w.
4
Step 4: Fill in the blank with w, so the factored form is w(k+y+w).
Knowledge Points Involved
1
Factoring Multiple Variable Terms Using Reverse Distributive Property
The reverse distributive property applies to multiple variable terms: ab + ac + ad = a(b + c + d). For terms kw, wy, w², the GCF is w, and factoring it out gives w(k+y+w).
2
Dividing Variable Terms with Exponents
When dividing variable terms with exponents, subtract the exponent in the denominator from the exponent in the numerator: x^m ÷ x^n = x^(m-n). For w²÷w, m=2, n=1, so w²÷w = w^(2-1) = w.
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