Question

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

Explanation:

Step1: Set up the box

The binomial \((-5x + 1)\) will be along the left side of the box, and \((2x - 4)\) will be along the top. So the left - hand column has \(-5x\) and \(1\), and the top row has \(2x\) and \(-4\).

Step2: Multiply the terms for each cell

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

Using the rule of exponents \(a^m\times a^n=a^{m + n}\), we have \((-5x)\times(2x)=- 10x^{2}\)

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

\((-5x)\times(-4) = 20x\)

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

\(1\times(2x)=2x\)

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

\(1\times(-4)=-4\)

Step3: Combine like terms

Now, we sum up all the terms from the cells: \(-10x^{2}+20x + 2x-4\)
Combine the \(x\) - terms: \(20x+2x = 22x\)
So the simplified form is \(-10x^{2}+22x - 4\)

Answer:

The simplified form of \((-5x + 1)(2x - 4)\) is \(-10x^{2}+22x - 4\) (and the box cells should have \(-10x^{2}\), \(20x\), \(2x\), \(-4\) in the appropriate positions)