Question

use the box method to distribute and simplify (4x + 2)(-5x + 1). drag and drop the terms to the correct locations of the table.
(4x + 2)(-5x + 1)
answer attempt 1 out of 2
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Explanation:

Step1: Create the box

We have a 2x2 box (since we are multiplying two binomials). The first binomial \((4x + 2)\) will be along the left - hand side of the box, and the second binomial \((-5x + 1)\) will be along the top of the box.

	\(-5x\)	\(1\)
\(2\)

Step2: Multiply the terms for each cell

• For the top - left cell (multiply \(4x\) and \(-5x\)):

Using the rule of exponents \(a^m\times a^n=a^{m + n}\), where \(a = x\), \(m=1\) and \(n = 1\), we have \(4x\times(-5x)=-20x^{2}\)

• For the top - right cell (multiply \(4x\) and \(1\)):

\(4x\times1 = 4x\)

• For the bottom - left cell (multiply \(2\) and \(-5x\)):

\(2\times(-5x)=-10x\)

• For the bottom - right cell (multiply \(2\) and \(1\)):

\(2\times1=2\)

Now our box looks like:

	\(-5x\)	\(1\)
\(2\)	\(-10x\)	\(2\)

Step3: Combine like terms

To simplify \((4x + 2)(-5x+1)\), we add up all the terms in the box: \(-20x^{2}+4x-10x + 2\)
Combine the \(x\) - terms: \(4x-10x=-6x\)

So the simplified form is \(-20x^{2}-6x + 2\)

Answer:

\(-20x^{2}-6x + 2\)