Find the value of the following expression if x=5, y=4, and z=1. 6 - (x-y) + y^2z + 3(x^2 - y^2)

Answer 1

Hi Mason...hope you had a great Turkey day and time off from school. Now...back on Monday...RIGHT!!

This is a great Algebra problem...and I'm glad you asked for some help.

This is also a great way to further develop your skill and understanding of PEMDAS...the correct order of operations when performing math operations with multiple variable.

Before we begin Mason...you should make sure you fully understand the terms I just used. It will make Algebra LESS complicated and it will give you a greater sense you can do these kinds of problems and be confident you are doing them correctly.. Also make sure you know what PEMDAS stands for...because if you don't...it can get complicated and frustrating.

Now here's the challenge for you Mason...I'm going to set this equation up for you give you an explanation for each step, but I won't calculate it for you....that is your job.

I won't be there during class time or a test to help you.

What I can do is give you the skill to begin answer these kinds of equations....so then during class time and tests...I will be there with you.

Okay here goes....so here's your equations:

Step 1: Write your equation 6 - (x - y) + y^2z + 3(x² - y²) = [some number]

when: x = 5, y = 4, z = 1

Step 2: For every variable (x, y, and z) substitute it for the known value, the re-write the equation:

For the x's: 6 - (5 - y) + y^2z + 3(5² - y²) =

For the y's: 6 - (5 - 4) + 4^2z + 3(5² - 4²) =

And last, for the z's: 6 - (5 - 4) + 4^2{1} + 3(5² - 4²) =

Now for the easy part...just follow the PEMDAS Order of Operations

Step 3: P stands for parenthesis...for start with the operations 'INSIDE' the parenthesis...and those are (5 - 4) 2(1) and (5² - 4²)

which will give you: (5 - 4) = 1 see note below

2(1) = 2

(5² - 4²) = 25 - 16 = 9 see note below

Note: though these two operations are subtraction and exponents, they are completed because they are inside a parenthesis.

Step 3: Now...put the new values back into the original equation:

6 - (1) + 4² + 3(9) = This is how your equation should look

You did the P part...parenthesis.

What comes next?

The E part which is for exponents!

Step 4: Let's do that....

6 - (1) + 4² + 3(9) = we'll do the 4² = 16 put it in the equation

6 - (1) + 16 + 3(9) =

We did the P and the E parts, what's next....that's right the M

So here we go...

Step 5: Complete the M part...which is:

6 - (1) + 16 + 3(9) = 3(9) = 27 this goes in the equation

6 - (1) + 16 + (27) = this is what it will look like

So we did the P part, the E part and the M part, what's next....that's right the D. Since there is no D part, we can skip that...

The only other parts are the A part and the S part.

Those are Step 5 and Step 6

This is where you will need to take over...I've given you the tools.

These kinds of problems ALL are approached the same way as long as you follow the PEMDAS Order of Operations...

The more you practice...the better you will improve your skill.

It would have been easy to give you the answer. I've given you the tools so you can now do these kind of problems yourself.

Connect with me if you need more assistance.

Have a great holiday.

J