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The 1st thing that I'm going to, in trying to simplify this expression, is to
look at each of the terms and figure out if I can squish it down at all. So
first, we have 15x squared, there's nothing that I can do to make that more
simple on its own, so I'm just going to rewrite it. Then 3x to the 7th, same
thing. Then I come to. Negative 7x times 2x. Now, there are definitely some
factors here that I can combine. If I rearrange the order of these things I can
put negative 7 and 2 next to each other and then the x's at the end. Negative 7
times 2 is negative 14, so I'll have a coefficient of negative 14. And then we
have times x times x and we know that x times x is just. x to the 2nd power. So
I can write that as well. Moving on we have negative 4 times 2x. We can again
combine the constant factors. So you have minus 8x, negative 5 times 4, 5 times
4 is 20. So we have negative 20 plus x times 3. We could just rearrange the
order of those two and then we have 3 times x. Which is just 3x, so plus 3x.
Great now each of the terms in and of itself is as simplified as it can get. The
next step is to figure out which terms are like terms. I'm also going to already
start writing like terms next to each other in a modified version of the
equation. We have 2x squared terms, only 1x to the 7th term, 2x to the 1st terms
and 1 constant term. Now I just need to combine the terms that I know are like
terms. Remember that we add the coefficients of like terms together and then
multiply by the variable. 15 minus 14 is 1, so we have 1 times x squared or just
x squared, 3x to the 7th is on its own, it's not combined with anything else.
Negative 8 plus 3 is negative 5, times the variable x, and then we have our
constant term. So this right here is our final answer. Our long, not very pretty
expression, has been squished down to be something much more managable.