Question

box method level 1 (guided)
score: 0/1 penalty: 1 off
question
use the box method to distribute and simplify $(-x - 1)(-4x + 6)$. drag and drop the terms to the correct locations of the table.
$(-x - 1)(-4x + 6)$
answer attempt 1 out of 2
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Explanation:

Step1: Set up the box

The two binomials are \(-x - 1\) (left side terms) and \(-4x + 6\) (top side terms). The box will have rows corresponding to \(-x\) and \(-1\), and columns corresponding to \(-4x\) and \(6\).

Step2: Multiply terms for each box cell

• Top - left cell (multiply \(-x\) and \(-4x\)): \((-x)\times(-4x)=4x^{2}\)
• Top - right cell (multiply \(-x\) and \(6\)): \((-x)\times6 = - 6x\)
• Bottom - left cell (multiply \(-1\) and \(-4x\)): \((-1)\times(-4x)=4x\)
• Bottom - right cell (multiply \(-1\) and \(6\)): \((-1)\times6=-6\)

Step3: Combine like terms

Now, we sum up all the terms from the box: \(4x^{2}-6x + 4x-6\). Combine the like terms \(-6x\) and \(4x\): \(-6x + 4x=-2x\). So the simplified form is \(4x^{2}-2x - 6\). But first, let's list the products for the box:

The box cells should have:

• First row (from \(-x\)): \(4x^{2}\) (with \(-4x\)) and \(-6x\) (with \(6\))
• Second row (from \(-1\)): \(4x\) (with \(-4x\)) and \(-6\) (with \(6\))

Answer:

The terms for the box (from top - left, top - right, bottom - left, bottom - right) are \(4x^{2}\), \(-6x\), \(4x\), \(-6\) respectively. And the simplified form of \((-x - 1)(-4x + 6)\) is \(4x^{2}-2x - 6\).