\(\displaystyle \small (x^4+3x^2-2)-(x^4-2x^2+7)=x^4+3x^2-2-x^4+2x^2-7\)

Combine like terms:
\(\displaystyle \small 5x^2-9\)

You can first rewrite the problem without the parentheses:

\(\displaystyle \left ( x^{3}+2x^{2}+5x \right )+\left ( x^{2}-3x+3 \right )=x^{3}+2x^{2}+5x +x^{2}-3x+3\)

Next, write the problem so that like terms are next to eachother:

\(\displaystyle x^{3}+2x^{2}+x^{2}+5x-3x+3\)

Then, add or subtract (depending on the operation) like terms. Remember that variables with different exponents are not like terms. For example, \(\displaystyle 2x^{2}\) and \(\displaystyle x^{2}\) are like terms, but \(\displaystyle x^{2}\) and \(\displaystyle 5x\) are not like terms:

\(\displaystyle x^{3}+3x^{2}+2x+3\)

\(\displaystyle \left ( 2x^{2}+4x+6 \right )-\left ( 3x^{2}+2x+10 \right )\)

When subtracting one polynomial from another, you must use distributive property to distribute the – sign:

\(\displaystyle -\left ( 3x^{2}+2x+10 \right ) = -3x^{2}-2x-10\)

\(\displaystyle -1*3x^{2}=-3x^{2}\)

\(\displaystyle -1*2x=-2x\)

\(\displaystyle -1*10=-10\)

Now, rewrite the entire problem without the parentheses:

 \(\displaystyle 2x^{2}+4x+6-3x^{2}-2x-10\)

Reorganize the problem so that like terms are together. Remember that variables with different exponents are not like terms. For example, \(\displaystyle 2x^{2}\) and \(\displaystyle -3x^{2}\) are like terms, but, \(\displaystyle 2x^{2}\) and \(\displaystyle 4x\) are not like terms:

 \(\displaystyle 2x^{2}-3x^{2}+4x-2x+6-10\)

Combine the like terms by adding or subtracting (depending on the operation):

\(\displaystyle -x^{2}+2x-4\)  

First simplify the parentheses to get:

\(\displaystyle x+xy-y+x^2-2y+5xy\)

Then combine like terms to get your answer of

 \(\displaystyle x^2+x+6xy-3y\)

To simplify the expression, combine like terms and eliminate the parentheses. Start by distributing the negative through the second parentheses.

\(\displaystyle \small \small 2x^2-5x+3 - (-3x^2)-(7x)-(-10)\)

\(\displaystyle \small \small \small 2x^2-5x+3 +3x^2-7x+10\)

Next, combine like terms.

\(\displaystyle \small 5x^2-12x+13\)

In previous problems, we used combining like terms to simplify. In this case, we first need to distribute in order to get rid of the parentheses.

Parentheses always indicate the operation multiplication. You multiply the number on the ouside of the parenthese by EVERY term inside the parentheses. In this case, you would multiply \(\displaystyle 4(2y) = 8y\) and \(\displaystyle 4(3) = 12\)

After this first step, you should have: \(\displaystyle 8y + 12 - 6y\)

Then, we will combine like terms. Here, the like terms are \(\displaystyle 8y\) and \(\displaystyle -6y\) (they both have the variable \(\displaystyle y\) and exponent 1). They combine into \(\displaystyle 8y - 6y = 2y\)

So the final answer is \(\displaystyle 2y + 12\)

(There is not anything you need to combine the 12 with, so you just leave it as is.)

The simplify this expression, combine like terms. Terms are like if they have the same variables and powers. To combine them, use addition and/or subtraction of the coefficients. The variables and powers do not change when you are combining.

\(\displaystyle -3b\) and \(\displaystyle -10b\) are like terms (both have the variable \(\displaystyle b\) and the exponent 1). To combine them, you do \(\displaystyle -3b-10b = -13b\)

\(\displaystyle 4a\) has the variable \(\displaystyle a\) and the exponent 1.

\(\displaystyle 6ab\) has the variable \(\displaystyle ab\) and the exponent 1

So \(\displaystyle 4a\) and \(\displaystyle 6ab\) they are NOT like terms - their variables are different. We cannot combine them. If you cannot combine terms, just leave them the same as they are and re-write them in you answer.

So the answer is: \(\displaystyle -13b + 4a + 6ab\)