Question

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

Answers

Answered by GPT 3.5
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
explain
Answered by GPT 3.5
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.

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