Question

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

Answer 1

`-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)`.