How do you combine like terms in #(5x ^ { 4} - 3x ^ { 2} + 6x - 3) + ( - 3x ^ { 4} + x ^ { 3} + 5x ^ { 2} - 7x + 3)#?

So, this is a pretty simple problem once you understand the foundations of such an expression.

Like terms are terms which have the same variables with the same exponents, such as #10x^6# and #7x^6#. To combine them, you just add or subtract, like so: #10x^6 - 7x^6 = 3x^6#. It really is that simple!

The only hiccup in this problem would have been if your #+# between the parentheses was a #-#. In that case, you would have first needed to change each of the signs on the terms in the second parentheses. As the problem is stated, that isn't necessary, and you're left with:

#5x^4 - 3x^2 + 6x - 3 - 3x^4 + x^3 + 5x^2 - 7x + 3#

If it's easier for you to visualize, you can always rearrange terms so like terms are beside each other, which would look like this:

#5x^4 - 3x^4 + x^3 - 3x^2 + 5x^2 + 6x - 7x - 3 + 3#

I know it looks like a lot, but if you visualize it in this manner it can become a lot simpler. At this stage, all you need to do is add and subtract accordingly, which leaves you with an answer of:

#2x^4 + x^3 + 2x^2 - x#

As a final note, typically you want to keep your exponent terms in descending order like the above because it makes it easier when using more advanced algebra skills.