Question

box method level 1 (guided)
score: 2/5 penalty: 1 off
question
use the box method to distribute and simplify \\((3x - 5)(3x + 1)\\). drag and drop the terms to the correct locations of the table.
\\((3x - 5)\left(3x + 1\
ight)\\)
answer attempt 1 out of 2
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Explanation:

Step1: Set up the box

We have two binomials \((3x - 5)\) and \((3x + 1)\). We can set up a 2x2 box where the terms of the first binomial are on the left side and the terms of the second binomial are on the top. So the left - hand side cells will have \(3x\) (top left of the left column) and \(- 5\) (bottom left of the left column), and the top - row cells will have \(3x\) (top left of the top row) and \(1\) (top right of the top row).

Step2: Multiply the terms for each cell

• Top - left cell: Multiply \(3x\) (from the left column) and \(3x\) (from the top row). Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), we have \(3x\times3x=(3\times3)x^{1 + 1}=9x^{2}\).
• Top - right cell: Multiply \(3x\) (from the left column) and \(1\) (from the top row). So \(3x\times1 = 3x\).
• Bottom - left cell: Multiply \(-5\) (from the left column) and \(3x\) (from the top row). We get \(-5\times3x=-15x\).
• Bottom - right cell: Multiply \(-5\) (from the left column) and \(1\) (from the top row). So \(-5\times1=-5\).

Step3: Combine like terms

Now we have the terms \(9x^{2}\), \(3x\), \(-15x\), and \(-5\) inside the box. The like terms are \(3x\) and \(-15x\). Combining them: \(3x-15x=(3 - 15)x=-12x\).

Step4: Write the simplified form

Now we combine all the non - like terms and the combined like terms. So the simplified form is \(9x^{2}-12x - 5\).

Answer:

The terms in the box are filled as follows:

• Top - left cell: \(9x^{2}\)
• Top - right cell: \(3x\)
• Bottom - left cell: \(-15x\)
• Bottom - right cell: \(-5\)

And the simplified form of \((3x - 5)(3x + 1)\) is \(9x^{2}-12x - 5\)