Question

Use the box method to distribute and simplify.(−5x+1)(2x−4)

Answer 1

explain

Answer 2

First, set up the box method with the terms (-5x + 1) along the top and (2x - 4) along the side:

| -5x | 1 |
------------------------------
2x | -10x^2 | 2x |
-4 | 20x | -4 |

Now, multiply the terms in each box and combine like terms:

-10x^2 + 2x + 20x - 4

-10x^2 + 22x - 4

So, the simplified expression is -10x^2 + 22x - 4.

Answer 3

To clarify the box method, we are essentially multiplying each term from one expression by each term from the other expression and organizing the results in a grid (or box).

In this case, we started by multiplying -5x from the first expression by 2x from the second expression to get -10x^2. Next, we multiplied -5x by -4 to get 20x. Then, we multiplied 1 from the first expression by 2x to get 2x, and finally, we multiplied 1 by -4 to get -4.

After multiplying and filling in the boxes, we combined like terms. In this case, we combined 2x and 20x to get 22x. The resulting expression after combining like terms is -10x^2 + 22x - 4.

This method helps to clearly see how each term from one expression interacts with each term from the other expression when multiplying them together.