# Need some help with simpliflying

#### maxmac97

##### New member
1 + (3 - 6 with exponent of 2 divide by 9) x 2 with an exponent of 2
1 + (3 - 4) X 2 with exponent of 2 1 - 1 x 2 with exponent of 2
Why did they get rid of the + and make it 1 - 1

2 + (9 -(7 - 3))
2 + (9 - 4)
2 + 5
On this problem they used the + and got rid of the -

#### topsquark

##### Full Member
Just to be clear you need to simplify the expression
$$\displaystyle 1 + \left ( 2 \cdot \left ( 3 - \dfrac{6^2}{9} \right ) \right ) ^2$$
Is this correct?
You are saying that this reduces to

$$\displaystyle 1 + (2 \cdot (3 - 4) )^2$$
Is this also correct? (If both guesses are correct then you have done the work correctly.)

Then we have
$$\displaystyle 1 + (2 \cdot -1 )^2$$

And the negative sign does indeed cancel out because you are squaring the negative 1.

Is there a typo in the suggested solutions? The first one is correct if we replace the 2 with a 1.

-Dan

#### Jomo

##### Elite Member
1 + (3 - 6 with exponent of 2 divide by 9) x 2 with an exponent of 2
1 + (3 - 4) X 2 with exponent of 2 1 - 1 x 2 with exponent of 2
Why did they get rid of the + and make it 1 - 1
There is a rule that says that you can change addition to subtraction or subtraction to addition as long as you change the sign of the 2nd number
Now you have 1 + (3 - 4) X 2 = 1 + (-1)x2 (note that (-1)X2 is a negative number) = 1 - (+1)X2 = 1 - (1)X2

#### Otis

##### Senior Member
... with exponent of 2 1 - 1 x 2 with exponent of 2 ...
Hello maxmac97. That's a confusing statement above, heh.

When typing math expressions, we use the caret symbol ^ to show exponents.

For example, we could type topsquark's LaTeX expression as shown below:

$$\displaystyle \displaystyle 1 + \left ( 2 \cdot \left ( 3 - \dfrac{6^2}{9} \right ) \right ) ^2$$

1 + [2*(3 - 6^2/9)]^2

We also type an asterisk * to show multiplication. (You'll see why, when you get to algebra, where the letter x represents a number, instead of a multiplication sign.)

In the forum guidelines, there's a link for Formatting Math as Text. It explains the conventions for typing math with a keyboard. Cheers

#### maxmac97

##### New member
The problem is 1 + (3 - 6^2 divide by 9 ) * 2^2
1 + ( 3 - 36 divide by 9 ) * 2^2
1 + ( 3 - 4 ) * 2^2
1 - 1 * 2^2
1 - 1 * 4
1 - 4
-3
I am still a little confused as to why they removed the + in problem one and used the + in problem two

Last edited:

#### Jomo

##### Elite Member
The problem is 1 + (3 - 6^2 divide by 9 ) * 2^2
1 + ( 3 - 36 divide by 9 ) * 2^2
1 + ( 3 - 4 ) * 2^2
1 - 1 * 2^2

I am still a little confused as to why they removed the + in problem one and used the + in problem two
Maybe you will see it better if we make the change later.

1 + ( 3 - 4 ) * 2^2
=1 + (-1)*4
=1 + (-4)
=1 - (+4) or simply 1-4
I too believe that the sign was changed too early but it does not matter as the outcome is the same.

#### Otis

##### Senior Member
The problem is 1 + (3 - 6^2 divide by 9 ) * 2^2
1 + ( 3 - 36 divide by 9 ) * 2^2
1 + ( 3 - 4 ) * 2^2
1 - 1 * 2^2
Your work is correct, up to the last line. (You don't need to type "divided by". We use a forward slash, to show division.)

1 + (3 - 36/9) * 2^2

1 + (3 - 4) * 2^2

1 + (-1)(4)

1 - 4

-3

I am still a little confused as to why they removed the + in problem one and used the + in problem two
In exercise #2 we have:

2 + (9 - (7 - 3))

Do the subtraction inside the innermost grouping symbols first (7-3):

2 + (9 - 4)

2 + 5

7

#### Otis

##### Senior Member
I completely forgot to mention the Order of Operations, a set of rules that establishes the order in which we do arithmetic steps. You can google it, to find lessons and examples.