Question

Adding and subtracting polynomials?

My book doesn't explain how to do this very well so I just need someone to explain how to do this question and then I think I can do the rest

Simplify: 2m^3n^3+9m^3n^3

Thank you :)

Answer 1

Notice if you let x = m^3n^3 you can replace all the copies of "m^3n^3" you see with "x"

So you go from this

2m^3n^3+9m^3n^3

to this

2x+9x

after doing those replacements.

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From here, you would see that there are like terms (both have a single x in them and nothing else). Because 2+9 = 11, we can say

2x + 9x = 11x

Answer 2

After all that, replace x with m^3n^3 to get this final answer: 11m^3n^3

Answer 3

This only works if we have like terms

2m^3n^3 and 9m^3n^3 are like terms because they

a) have the same variables (m & n)

AND

b) the exponents over the variables are the same (the exponents over the m must be the same, the exponents over the n must be the same). Something like 2m^2n^3 and 9m^3n^3 would not be considered like terms because the exponents over the m are not the same. However 2m^2n^3 and 9m^2n^3 are like terms.

Answer 4

Hopefully all this is making sense

Answer 5

@jim_thompson5910 Makes perfect sense. Thank you for explaining! I think I got it now. Thank you again for your help

Answer 6

you're welcome