Question

box method level 1 (guided)
score: 3/5 penalty: 1 off
question
use the box method to distribute and simplify \\((2x + 4)(-4x - 1)\\). drag and drop the terms to the correct locations of the table.
\\((2x + 4)\left(-4x - 1\
ight)\\)
answer attempt 1 out of 2
you must answer all questions above in order to submit.

Explanation:

Step1: Set up the box

The binomial \((2x + 4)(-4x - 1)\) can be represented in a 2x2 box. The first binomial \((2x + 4)\) will be along the left side (rows), and the second binomial \((-4x - 1)\) will be along the top (columns). So the left - hand side cells (rows) are \(2x\) and \(4\), and the top - hand side cells (columns) are \(-4x\) and \(-1\).

Step2: Multiply to fill the box

• Multiply the term in the first row (\(2x\)) and the first column (\(-4x\)): \(2x\times(-4x)=-8x^{2}\)
• Multiply the term in the first row (\(2x\)) and the second column (\(-1\)): \(2x\times(-1)=-2x\)
• Multiply the term in the second row (\(4\)) and the first column (\(-4x\)): \(4\times(-4x)=-16x\)
• Multiply the term in the second row (\(4\)) and the second column (\(-1\)): \(4\times(-1)=-4\)

Step3: Combine like terms

Now, we have the terms \(-8x^{2}\), \(-2x\), \(-16x\), and \(-4\) in the box. Combine the like - terms (the \(x\) terms): \(-2x-16x=-18x\)

Step4: Write the simplified form

The simplified form of \((2x + 4)(-4x - 1)\) is the sum of the terms in the box: \(-8x^{2}-18x - 4\)

Answer:

The simplified form of \((2x + 4)(-4x - 1)\) using the box method is \(-8x^{2}-18x - 4\). The terms in the box are filled as follows:

	\(-4x\)	\(-1\)
\(4\)	\(-16x\)	\(-4\)

And after combining like terms, the final answer is \(\boldsymbol{-8x^{2}-18x - 4}\)