Not sure where to start

Question

sorryimfrankie · Answer

attachment

mathstudent55 · Answer

Do you know how to tell the degree of a polynomial?

sorryimfrankie · Answer

I think so. its just the highest exponent, right?

mathstudent55 · Answer

Its the same as the highest degree of any term in that polynomial.
The degree of a term is the sum of the exponents of all variables in the term.

mathstudent55 · Answer

Look at the first polynomial term by term.

Term $3x^5y$ has degree 6. 
The exponent of x is 5, and the exponent of y is 1, and 5 + 1 = 6

The degree of term $-2x^3 y^4$ is 7 since 3 + 4 = 7.

The degree of term $-7xy^3$ is 4 since 1 + 3 = 4.

The term with highest degree has a degree of 7, so the entire polynomial has degree 7.

Ok so far?

sorryimfrankie · Answer

Yup :)

mathstudent55 · Answer

Now let's see when you add the polynomials together.
You have to add like terms together.
Like terms are terms that have the same variables and the same exponents.

sorryimfrankie · Answer

And its the same with the second polynomial, right? The degree is 7?

mathstudent55 · Answer

Yes, you are correct.

sorryimfrankie · Answer

Okay, I'll try adding the terms together. This is where I get a little confused.

mathstudent55 · Answer

That's why I'm here. To de-confuse you.

mathstudent55 · Answer

Start with the addition of the polynomials:

$(3x^5 y - 2x^3y^4 -7xy^3) + (-8x^5y + 2x^3y^4 + xy^3)$

mathstudent55 · Answer

Since we have an addition, we can remove both sets of parentheses since they are unnecessary.

$=3x^5 y - 2x^3y^4 -7xy^3 + (-8x^5y) + 2x^3y^4 + xy^3$

Now we can group the like terms together.

$=3x^5 y + (-8x^5y) - 2x^3y^4 + 2x^3y^4 -7xy^3 + xy^3$

Now can you finish the sum by combining like terms together?

sorryimfrankie · Answer

$$-5 - 4x^3y^4 - 8xy^3?$$

mathstudent55 · Answer

No.
Look below.

$=\color{red}{3x^5 y + (-8x^5y)} \color{blue}{- 2x^3y^4 + 2x^3y^4} \color{green}{-7xy^3 + xy^3}$

$=\color{red}{3x^5 y -8x^5y} \color{blue}{- 2x^3y^4 + 2x^3y^4} \color{green}{-7xy^3 + xy^3}$

$=\color{red}{-5x^5 y } \color{blue}{} \color{green}{-6xy^3 }$

mathstudent55 · Answer

Notice that the terms with $x^3y^4$ added to zero, so the highest degree of a term now is 6.

mathstudent55 · Answer

The sum is of degree 6.

sorryimfrankie · Answer

Oooooh, okay, I get it now. So, now our next step will be to subtract the polynomials?

mathstudent55 · Answer

Correct.
Let me set it up.

sorryimfrankie · Answer

Thanks :)

mathstudent55 · Answer

We have the same two polynomials with a minus sign between them since we are now subtracting.

$(3x^5 y - 2x^3y^4 -7xy^3) - (-8x^5y + 2x^3y^4 + xy^3)$

mathstudent55 · Answer

You can start by removing the first set of parentheses since it is unnecessary.

To remove the second set of parentheses, you need to distribute the minus sign to its left by every term inside the second set of parentheses. That means every sign inside the second set of parentheses changes.

sorryimfrankie · Answer

$$11x^5y - 4x^3y^4 - 8xy^3$$

sorryimfrankie · Answer

is this right? sorry for jumping ahead, i'm on a timed assignment

mathstudent55 · Answer

Correct.
What is the highest degree of a term?

sorryimfrankie · Answer

7, right?

mathstudent55 · Answer

Correct.
That is the same as the degree of the difference.

mathstudent55 · Answer

Degree of sum: 6
Degree of difference: 7

mathstudent55 · Answer

Great job!

sorryimfrankie · Answer

Thanks so much, you're a lifesaver! :)

mathstudent55 · Answer

You're welcome.