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

2 Answers
smendyka
Mar 17, 2018

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)

Fabio
Mar 17, 2018

(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)

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