Question

How do you evaluate `(2x - 5y ) ( 7x - 4y )`?

Answer 1

`14x^2 - 43xy + 20y^2`

Explanation:

To solve this problem, we have to distribute everything out. You've probably heard of using FOIL to solve these problems, but I prefer using rainbow.

Multiply `2x` with `7x` and get `14x^2`.

Multiply `-5y` with `7x` and get `-35xy`.

Multiply `-4y` with `2x` and get `-8xy`.

Multiply `-5y` with `-4y` and get `20y`.

When we combine them all together, we get this:
`14x^2 - 35xy - 8xy + 20y^2`

Now we need to combine the "like terms." In this case only `-35xy` and `-8y` are "like terms," so we add them together and we get `-43xy`. Here is the final answer below:
`14x^2 - 43xy + 20y^2`