How do you simplify (x + 2) ^ { 2} - 5x - ( x ^ { 2} - 13)?

1 Answer
Sep 15, 2017

-x+17

Explanation:

(x+2)^2-5x-(x^2-13)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
That's the whole long expression.

First, I will focus on (x+2)^2.
So the first thing you have to do is to apply this rule.
(a+b)^2=a^2+2ab+b^2

So, using that rule on (x+2)^2, it would be:
x^2+2x*2+2^2

Now we will simplify that expression. (x^2+2x*2+2^2)
2*2=4
So, x^2+color(blue)4color(blue)x+2^2 would be the new expression.

But, 2^2=4 so the expression after simplifying would be x^2+4x+4.

Now, stick it into the rest of the WHOLE expression.
x^2+4x+4-5x-(x^2-13)
Now we will focus on the rightmost side (-(x^2-13))

Distribute brackets/parentheses.
-(x^2)-(-13)
Now remember this: -(a)=-a and -(-b)=+b.
In this case, a represents x^2 and b represents 13.
That means -(x^2)-(-13) would become -x^2+13.
Stick the whole expression together and you get

x^2+4x+4-5x-x^2+13.

Wow. That's a long expression. Let's simplify it.
First, we need to group like terms.

x^2+4x+4-5x-x^2+13 to
x^2-x^2+color(blue)4color(blue)xcolor(blue)-color(blue)5color(blue)x+4+13

You see the blue numbers/symbols?
Let's simplify those:
4x-5x=-x.
Now we can replace 4x-5x with -x.

So, the expression would be color(blue)x^color(blue)2color(blue)-color(blue)x^color(blue)2-x+4+13.

Let's simplify the blue numbers/symbols again.
x^2-x^2=0.

The final expression would be -x+color(blue)4color(blue)+color(blue)13.

Add the blue numbers:
14+3=17

Therefore, -x+17 is the simplified expression of
(x+2)^2-5x-(x^2-13).