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help with polynomials?

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(3AB+Asquared +Bsquared) + (4Bsquared - 3AB + 3Asquared)
hunger games :D

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can you guys help me
\((3AB + A^2 + B^2) + (4B^2 - 3AB + 3A^2)\) Add together like-terms. \(kA^2 + hA^2 = (k + h)A^2\), \(kAB + hAB = (k + h)AB\), etc.
You can reorder the expression using the commutative and associative properties of addition (nothing multiplied to the parentheses, its just addition so we can remove them): \((3AB - 3AB) + (A^2 + 3A^2) + (B^2 + 4B^2)\) Then you just add the coefficients together. Makes sense?
it helps a bit
Then by factoring: \((3 - 3)AB + (1 + 3)A^2 + (1+4)B^2\) Simplifying, we get \(0AB + 4A^2 + 5B^2 \\ = \mathbf{4A^2 + 5B^2}\)
yah thats right i get it thanks
The less rigorous approach is pretty much just looking at the like terms, usually faster than doing the "pair the like terms, factor, and simplify" stuff: Once you simplify it to only addition and subtractions: \(\color{green}{3AB} + \color{purple}{A^2} + \color{red}{B^2} + \color{red}{4B^2} \color{green}{- 3AB} + \color{purple}{3A^2}\) The \(3AB\) and \(-3AB\) cancel, add coefficients of \(A^2\) and \(B^2\) terms You're welcome. :)

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