simplify 5x^{3} y^{2} - 7x^{3} y^{2}

Question

mathstudent55 · Answer

Terms that have the same variable parts are like terms and can be combined together.
For example, 5a - 7a = -2a

anonymous · Answer

is the answer -2x^3y^2?

mathstudent55 · Answer

correct
since the variable parts are the same, x^3y^2, the terms are like terms and can be combined just like you did
Good job!

anonymous · Answer

i have another question

mathstudent55 · Answer

go ahead

anonymous · Answer

how do i simplify (3m^2+2m-8) + (4m^2-5m+6)

anonymous · Answer

?

mathstudent55 · Answer

You have two trinomials being added together.

anonymous · Answer

@mathstudent55  why does your smartscore stick at 99 lol

mathstudent55 · Answer

The first step is to drop both pairs of parentheses. Since there is no minus sign outside to the left of each set of parentheses, the parentheses are unnecessary.

mathstudent55 · Answer

I have no idea how the smart score stuff works.

anonymous · Answer

would it be 7m^2...

anonymous · Answer

i dont know what to do next

mathstudent55 · Answer

(3m^2+2m-8) + (4m^2-5m+6)
= 3m^2+2m-8 + 4m^2-5m+6
Now you have the same problem without the parentheses.
You can only add like terms together.
Like terms have exactly the same variable part.
3m^2 and 4m^2 are like terms.

mathstudent55 · Answer

Let me now rearrange it to make it clearer for you. I'l group the pairs of like terms together.

anonymous · Answer

it would be 7m^2 right?

mathstudent55 · Answer

(3m^2+2m-8) + (4m^2-5m+6)
= 3m^2+2m-8 + 4m^2-5m+6
= 3m^2 + 4m^2 + 2m - 5m - 8 + 6

mathstudent55 · Answer

Yes, you start with 7m^2. Then combine the two terms with m, then combine the two terms without variable.

mathstudent55 · Answer

I have to go now. I'll be back in around 15 minutes.

anonymous · Answer

ok thanks

mathstudent55 · Answer

I'm back. Did you finish it?

anonymous · Answer

is it 7m^2-3m-14?

mathstudent55 · Answer

Notice you have -8 +6, not +8 +6

anonymous · Answer

so what would it be?

mathstudent55 · Answer

3m^2 + 4m^2 + 2m - 5m - 8 + 6
= 7m^2 - 3m - 2
You got the m^2 part and the m part correct.

anonymous · Answer

u teach me more than my math teacher

mathstudent55 · Answer

thanks

mathstudent55 · Answer

Do you have more questions? I can help with for another 15 minutes or so. Then I have to go.

anonymous · Answer

how do i solve 3n(4n^2+5n?

mathstudent55 · Answer

There is a close parentheses missing. Where does it go?

mathstudent55 · Answer

Is it 3n(4n^2+5n)?

anonymous · Answer

yes

mathstudent55 · Answer

In this case, you need to use the distributive porperty to distribute 3n by what is inside the parentheses.

mathstudent55 · Answer

Think of this simple example of the distributive property:
What is 2(3 + 4) using the distributive property?
2(3 + 4) = 2*3 + 2*4 = 6 + 8 = 14
What is 2(3 + 4) without using the distributive property?
2(3 + 4) = 2(7) = 14
As you can see the result, 14, is the same.

mathstudent55 · Answer

The second method involved 1 addition, 3 + 4 = 7, then one multiplication, 2 * 7 = 14.
It is easier to do than to do it with the distributive property.

mathstudent55 · Answer

The distributive property is useful when you can't combine what is inside the parentheses because they are not like terms.
Look at this example:
What is 2(a + 3) = ?

mathstudent55 · Answer

You can't do a + 3 first since a and 3 are not like terms, so the only way to simplify 
2(a + 3) is by using the distributive property.
Using the distributive property, you get
2(a + 3) = 2*a + 2*3 = 2a + 6
That is as simplified as you can get since 2a and 6 are not like temrs and can't be added together.

mathstudent55 · Answer

Now let's get back to our problem:
3n(4n^2+5n)
The terms inside the parentheses are not "like terms" since n^2 and n are not the same.
The terms inside the parentheses cannot be added together.
The only way to simplify this expression is by using the distributive property.
3n(4n^2+5n) =
3n * 4n^2 + 3n * 5n =
12n^3 + 15n^2

mathstudent55 · Answer

You haven't answered in a while. I hope I haven't put you to sleep.
Are you following this?

anonymous · Answer

haha sorry my computer died

mathstudent55 · Answer

Take a while to read what I wrote and ask any questions you may have.

anonymous · Answer

i cant combine 12n^3 and 15n^2 because the exponents are different right?

mathstudent55 · Answer

correct

anonymous · Answer

how would i solve 4k^2(3-4k)

anonymous · Answer

?

mathstudent55 · Answer

Once again, since you can't combine the terms inside the parentheses bec thay are not like terms, you must use the distributive property.
4k^2(3-4k) =
4k * 3 - 4k * 4k =
12k - 16k^2

anonymous · Answer

how do i solve 18s-63?

mathstudent55 · Answer

What exactly are the instructions with this problem?

mathstudent55 · Answer

You can't combine together 18s and - 63 because they are not like terms.