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Trying to make some sense of this seemingly easy problem:

Find the difference of $4b^3 + 6b - 7$ and $-12b^2 + 11b + 5$.

Trying to prepare for my Algebra 1 final, which is a week from Thursday, and I came across this problem in the textbook. I have looked at previous problems and there just does not appear to be any this long. Usually you'd expect to find some similar problems, am I correct? But not in this case, it baffled me. So I'm hoping I can get some help and hopefully the question can be helpful to others as well. And my goal here isn't to just have it answered, but rather, I want to understand what I am doing so that when these kind of problems come up on the final, I will not panic but actually have some knowledge of how to handle them rather than being overwhelmed by the number of variables and exponents.

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    $\begingroup$ I am sure you have worked with polynomials in Algebra 1. Could you do this problem if the $b$ were an $x$? It's the same problem. $\endgroup$
    – Ethan Bolker
    Commented Apr 15 at 14:44
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    $\begingroup$ I know what difference is, but thank you. And comes off as long to me because of the number of variables and exponents. It may not be a particularly long equation but it comes off that way in my head due to just how many variables and exponents are in each term. And I'm trying to figure out how to get beyond that. $\endgroup$
    – YourLordJoyBoy
    Commented Apr 15 at 14:47

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The difference is the quantity $4b^3+6b+7-(-12b^2+11b+5)$, so the answer is $4b^3+12b^2-5b+2$.

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