Question

question
use the box method to distribute and simplify $(-2x - 6)(-4x + 1)$. drag and drop the terms to the correct locations of the table.
$\left(-2x - 6\
ight)\left(-4x + 1\
ight)$

	$-4x$	$1$
$-6$	$\square$	$\square$

try
answer attempt 1 out of 2
you must answer all questions above in order to submit.

Explanation:

Step1: Multiply -2x and -4x

To find the term for the first cell (row: -2x, column: -4x), we multiply \(-2x\) and \(-4x\). Using the rule of exponents \(a^m \cdot a^n = a^{m + n}\) and the sign rule (negative times negative is positive), we get \((-2x) \times (-4x) = 8x^2\).

Step2: Multiply -2x and 1

For the second cell (row: -2x, column: 1), we multiply \(-2x\) and \(1\). The product is \((-2x) \times 1 = -2x\).

Step3: Multiply -6 and -4x

For the third cell (row: -6, column: -4x), we multiply \(-6\) and \(-4x\). Using the sign rule (negative times negative is positive), we get \((-6) \times (-4x) = 24x\).

Step4: Multiply -6 and 1

For the fourth cell (row: -6, column: 1), we multiply \(-6\) and \(1\). The product is \((-6) \times 1 = -6\).

Answer:

The terms for the table (from top - left to bottom - right, then top - right to bottom - right) are \(8x^2\), \(-2x\), \(24x\), \(-6\). So the filled table cells are:

• Row \(-2x\), Column \(-4x\): \(8x^2\)
• Row \(-2x\), Column \(1\): \(-2x\)
• Row \(-6\), Column \(-4x\): \(24x\)
• Row \(-6\), Column \(1\): \(-6\)

If we were to simplify the entire expression after filling the table, we combine like terms: \(8x^2-2x + 24x-6=8x^2 + 22x-6\), but for the table filling, the terms are \(8x^2\), \(-2x\), \(24x\), \(-6\) in their respective cells.