Question

How do you factor `(x+2)^2 -5(x+2)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the term on the left as:

`(x + 2)(x + 2) - 5(x - 2)`

Next, factor out a common term of `(x - 2)` giving:

`((x + 2) - 5)(x - 2) =>`

`(x + 2 - 5)(x - 2) =>`

`(x - 3)(x - 2)`

Answer 2

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

Explanation:

First we expand the `(x+2)^2` which looks like `(x+2)(x+2)`

Next we just multiply it out which will give us
`x^2+4x+4`

Now that we know
`(x+2)^2 = x^2+4x+4`

We can do the other part which is `5(x+2)`
Which is `(5x+10)`
Now we know `5(x+2)=(5x+10)`

Now we can write the problem out expanded
`x^2+4x+4-(5x+10)`

NOTICE THE NEGATIVE SIGN IN FRONT OF THE PARENTHESES.
We have to distribute this negative to all terms in the parentheses.
Which gives us
`x^2+4x+4-5x-10`

Now we just combine like terms
`x^2-1x-6`

Now we need 2 numbers that multiply to `-6` and add up to `-1`
These numbers are `-3` and `2`

Notice `-3*2=-6`
And `-3+2=-1`

So we then get
`(x-3)(x+2)`