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Question Use the box method to distribute and simplify \( (3 x-5)(3 x+1) \). Drag and drop the terms to the correct locations of the table. \[ (3 x-5)(3 x+1) \] \[ \text { Show fomptes } \] Answer Attempt out of 2

Ask by Franklin Pope. in the United States
Feb 25,2025

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Tutor-Verified Answer

Answer

(3x – 5)(3x + 1) = 9x² – 12x – 5

Solution

Step 1: Set up the Box Draw a 2×2 grid. Label the top columns with the terms from the second factor (3x and +1) and the rows with the terms from the first factor (3x and –5): 3x | +1 ------------------------- 3x | (3x)(3x) | (3x)(+1) ------------------------- –5 | (–5)(3x) | (–5)(+1) Step 2: Fill in Each Box • Top left: (3x)(3x) = 9x² • Top right: (3x)(+1) = 3x • Bottom left: (–5)(3x) = –15x • Bottom right: (–5)(+1) = –5 Step 3: Combine Like Terms Add the middle terms:   3x + (–15x) = –12x So the expression simplifies to:   9x² – 12x – 5 Final Answer: (3x – 5)(3x + 1) = 9x² – 12x – 5

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To use the box method for distributing \( (3x - 5)(3x + 1) \), you can create a 2x2 grid (box) where each part of the first binomial is on one side and each part of the second binomial is on the other. Fill in the box with the products of each pair of terms: | | \(3x\) | \(-5\) | |---------|------------|------------| | \(3x\) | \(9x^2\) | \(-15x\) | | \(1\) | \(3x\) | \(-5\) | Now, you simply combine the products. This gives you: \[ 9x^2 - 15x - 5 \] So the final simplified result is: \[ 9x^2 - 15x - 5 \]

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