Question

How do you simplify `(x+3)(x+2)`?

Answer 1

`x^2 + 5x + 6`

Explanation:

`(x+3)(x+2)`

To simplify this, we use the distributive method called FOIL, as shown here:

Following this image, first multiply the `color(red)("firsts")`:
`color(red)(x * x) = x^2`

Then the `color(purple)("outsides")`:
`color(purple)(x * 2) = 2x`

Then the `color(darkturquoise)("insides")`:
`color(darkturquoise)(3 * x) = 3x`

And finally the `color(limegreen)("lasts")`:
`color(limegreen)(3 * 2) = 6`

Now combine all of these:
`x^2 + 2x + 3x + 6`

We can still combine `color(blue)(2x + 3x)` because they are like terms. Therefore, the final answer is:
`x^2 + 5x + 6`

Hope this helps!