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Complete the Expression with Distributive Property: k(8 + 3 + k) = 8k + 3k + ?
Mathematics
Grade 7
Question Content
Use the distributive property to complete the statement: k(8 + 3 + k) = 8k + 3k + ____
Correct Answer
k²
Detailed Solution Steps
1
Step 1: Recall the distributive property for multiple terms: c(a+b+d) = ca + cb + cd.
2
Step 2: Apply the property to k(8+3+k): multiply k by each term inside the parentheses. k×8 = 8k, k×3 = 3k, k×k = k².
3
Step 3: Fill in the blank with k².
Knowledge Points Involved
1
Distributive Property with Variable Terms in Parentheses
The distributive property applies when parentheses include variable terms: k(a+b+k) = ka + kb + k². When multiplying a variable by itself, k×k = k², following exponent rules for like bases.
2
Exponent Rule for Multiplying Like Bases
When multiplying two terms with the same base, add the exponents: x^m × x^n = x^(m+n). For k×k, m=1, n=1, so k×k = k^(1+1) = k².
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