Question

use the box method to distribute and simplify $(-3x - 2)(-6x - 5)$. drag and drop the term to the correct locations of the table.
$(-3x - 2)(-6x - 5)$
answer attempt 1 out of 2
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Explanation:

Step1: Create the box (table)

We have two binomials \((-3x - 2)\) and \((-6x - 5)\). The box method (also known as the area method) for multiplying two binomials \((a + b)(c + d)\) involves creating a table with two rows (corresponding to the terms of the first binomial) and two columns (corresponding to the terms of the second binomial). Here, the first binomial is \(-3x - 2\) (so rows: \(-3x\) and \(-2\)) and the second binomial is \(-6x - 5\) (so columns: \(-6x\) and \(-5\)).

	\(-6x\)	\(-5\)
\(-2\)	\((-2)(-6x)\)	\((-2)(-5)\)

Step2: Calculate each cell

• For the cell with \(-3x\) and \(-6x\): \((-3x)(-6x)=18x^{2}\) (using the rule \(a^{m}\cdot a^{n}=a^{m + n}\) and \((-a)(-b)=ab\))
• For the cell with \(-3x\) and \(-5\): \((-3x)(-5) = 15x\) (since \((-a)(-b)=ab\))
• For the cell with \(-2\) and \(-6x\): \((-2)(-6x)=12x\) (since \((-a)(-b)=ab\))
• For the cell with \(-2\) and \(-5\): \((-2)(-5)=10\) (since \((-a)(-b)=ab\))

Step3: Combine like terms

Now, we sum up the terms from the table. The terms are \(18x^{2}\), \(15x\), \(12x\), and \(10\). The like terms are \(15x\) and \(12x\). Combining them: \(15x+12x = 27x\). So the simplified form is \(18x^{2}+27x + 10\)

Answer:

The product \((-3x - 2)(-6x - 5)\) simplifies to \(18x^{2}+27x + 10\)