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# how do i smiplify expressions using the order of operations

Hi Deedee. Feel free to post a sample of the type of problems you are working on.

One helpful way to remember the order of operations is PEMDAS.

P is for parentheses. Things insided parentheses should be expanded or simplified first.

E is for exponents. Exponents are applied to their bases next.

M and D are for multiplication and division. These operations should be done left to right, next.

A and S are for addition and subtraction. These are the final operations to tod, left to right.

Here is an example problem.

3(3+x-4)2 = (8x2+6)/2+7

First, look inside each set of parentheses. The one the left can be simplified:

3(x-1)2 = (8x2+6)/2+7

The 3 and the 4 inside parentheses are like terms. I combined them. We can’t do anything with the x, yet. For the parentheses on the right, we cannot combine anything because 8x2 and 6 are not like terms.

The next operation we do would be to open those parentheses. On the left, two things are acting on the expression in the parentheses. There is a 3 being multiplied by everything inside and there is an exponent of 2. We do the exponent first according to PEMDAS.

3(x-1)(x-1) = (8x2+6)/2+7

3(x2-2x+1) = (8x2+6)/2+7

Then we distribute the 3:

3x2-6x+3 = (8x2+6)/2+7

The left side is done for a while. On the right side there is one operation on the expression inside the parentheses: division by 2. We distribute that division.

3x2-6x+3 = 4x2+3 +7

The only operations remaining are addition and subtraction.

3x2-6x+3 = 4x2+10

Now we are done simplifying with the order of operations. You will notice that this is an equation with x2, x, and numeric terms. We call this a quadratic equation and if we set it up right, we can solve with the quadratic formula. (Don’t worry if you haven’t gotten to this yet. PEMDAS works even if you don’t have any x2 terms.)

I will move all the terms to the right by adding their opposites to both sides.

3x2 -6x +3 = 4x2+10

-3x2 +6x -3 -3x2 +6x -3

0 = x2+6x+7 (A quadratic equation).

This is relatively basic and uses the following priorities:

Parenthesis

Exponent

Multiply / Divide

or PEMDAS. So something to simplify may be:

3^3x2+4=? Note that x is a multiplication sign

27x2+4 no parenthesis so exponents first

52+4 multiplication next