How do you simplify Polynomials?

Question

2x^3+ 3x^3 + (-6x^3)


4ab^2 - 3ab^2


3x^2y + 4 - 3x^2y


n^4 * n^3 * n^2

Answer 1

You simplify polynomials by combining the like terms. Think about it like this: It doesn't make any sense to say that a pet shop has 6 dogs, then 4 more dogs, then 2 more dogs. It makes sense to just combine all the dogs together and say there's 6 +4 + 2 or 12 dogs. If there were some cats, we wouldn't combine the cats and dogs together, we'd say that there are x number of dogs and y number of cats.

Polynomials are the same way. Just group all of the x's together, all of the x^2 terms together, all of the xy terms together, etc. You cannot combine terms that have different variables or powers of variables in them. This means you cannot combine 4x + 5y, nor can you combine 5x + 7x^2.

So for your problems:

2x^3 + 3x^3 + (-6x^3)
(2 + 3 + -6)x^3
-1x^3
Since all terms have the same variable and the same power, you can combine them all. Just add 2 + 3 + (-6) and attach the x^3 when you're done.

4ab^2 - 3ab^2
(4 - 3)ab^2
1ab^2

Same story as #1



3x^2y + 4 - 3x^2y
(3 - 3)x^2y + 4
0x^2y + 4
4

The four does not combine with the other terms, since is does not have the x squared y after it. Since there are 0 x^2y terms left after we're done, we don't even need to mention it in the answer. It's like if that pet store has no snakes, you don't say it has 20 dogs, four cats and no snakes; you just don't mention the snakes.



n^4 * n^3 * n^2

Multiplying is a little different. When you multiply terms together, you can combine anything. Remember that exponents tell you how many of each variable are being multiplied together:

n^4 = n * n * n * n * n
n^3 = n * n * n
n^2 = n * n

So to multiply these all together, we just combine all of the variables into one giant multiplication problem.

n^4 * n^3 * n^2
(n * n * n * n) * (n * n * n) * (n * n)
n * n * n * n * n * n * n * n * n
n^9

You're other option is just to add all of the exponents together when ever you multiply the same variables together.

n^4 * n^3 * n^2
n^(4 + 3 + 2)
n^9

Good luck and have fun!

Answer 2

Simplifying polynomials is a process of examination, and careful re-writing. Experience helps.

2x^3+ 3x^3 + (-6x^3)
(2)x^3 + (3)x^3 + (-6)x^3
all three terms have a (x^3) factor, these can be collected
[ (2) + (3) + (-6) ] x^3
[ (2) + (3) - (6) ] x^3
[ 2 + 3 - 6 ] x^3
[ -1 ] x^3

4ab^2 - 3ab^2
(4)ab^2 - (3)ab^2
[ (4) - (3) ] ab^2
[ 4 - 3 ] ab^2
[ 1 ] ab^2


3x^2y + 4 - 3x^2y
the middle term does not have the common (x^2y) so keep it separate
[ 3x^2y - 3x^2y ] + 4
now simplify the part in the square brackets
[ (3)x^2y - (3)x^2y ] + 4
[ [ (3) - (3) ] x^2y ] + 4
[ [ 3 - 3 ] x^2y ] + 4
[ [ 0 ] x^2y ] + 4
4

n^4 * n^3 * n^2
here everything is being multiplied so you can add the exponents
n^9

BTW, with practice one can "simplify by examination". I would not go through every step if I had to simplify these problems for my own use. I can do some of the steps in my head. But until all the rules and tricks are automatic, it is better to work a little slower and more carefully and get them right.

Answer 3

2x^3+3x^3+(-6x^3)= -x^3


4ab^2 - 3ab^2 = ab^2

3x^2y+4-3x^2y = 4

n^4 * n^3 * n^2 = n^9

Answer 4

2x^3+3x^3-6x^3=-x^3
4ab^2-3ab^2=ab^2
3x^2y+4-3x^2y=4
n^4 x n^3 x n^2=n^9

Answer 5

-x^3

ab^2

4

n^9

for 1 to 3, just add same terms and follow the rules of how to add polynomials

for number 4, just multiply the base number and add the exponent. that is how to multiple polynomials

i hope it helps