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My DXL Learning Assessment Analytics suxth orade +2.6 rector numercal exsressons using the distrisutive propety maz Factor \( 56+32 \). Write your answer in the form \( a(b+c) \) where \( a \) is the GCF of 56 and 32 . (D) Submit

Ask by Wood Henry. in the United States
Mar 16,2025

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Tutor-Verified Answer

Answer

Factor \(56 + 32\) using the distributive property with the GCF of 8. Final answer: \[ 8(7 + 4) \]

Solution

1. Identify the greatest common factor (GCF) of \(56\) and \(32\). \[ \text{GCF}(56, 32) = 8 \] 2. Express each term as a product involving \(8\): \[ 56 = 8 \times 7, \quad 32 = 8 \times 4 \] 3. Factor out the common factor \(8\) using the distributive property: \[ 56 + 32 = 8 \times 7 + 8 \times 4 = 8(7+4) \] Final answer: \[ 8(7+4) \]

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Bonus Knowledge

To factor \( 56 + 32 \) using the distributive property, first find the greatest common factor (GCF) of 56 and 32. The GCF is 8. Then, rewrite the expression by factoring out 8: \[ 56 + 32 = 8(7 + 4) \] So, the final answer is \( 8(7 + 4) \). Factoring is a skill that develops with practice! Try visualizing the numbers as groups of candies or toys. Imagine you have 56 candies and 32 more, and you want to group them evenly. Once you picture it, how you break down the numbers becomes more intuitive! Want to dig deeper? Check out some online math resources or educational YouTube channels that specialize in fun, engaging math tutorials. Watching others solve similar problems can reinforce your understanding and help you see the practical applications of factoring in everyday life—like budgeting or organizing!

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