countonme123 3 years ago help with polynomials?

1. countonme123

(3AB+Asquared +Bsquared) + (4Bsquared - 3AB + 3Asquared)

2. alexwee123

hunger games :D

3. countonme123

:)

4. countonme123

can you guys help me

5. AccessDenied

$$(3AB + A^2 + B^2) + (4B^2 - 3AB + 3A^2)$$ Add together like-terms. $$kA^2 + hA^2 = (k + h)A^2$$, $$kAB + hAB = (k + h)AB$$, etc.

6. AccessDenied

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?

7. countonme123

it helps a bit

8. AccessDenied

Then by factoring: $$(3 - 3)AB + (1 + 3)A^2 + (1+4)B^2$$ Simplifying, we get $$0AB + 4A^2 + 5B^2 \\ = \mathbf{4A^2 + 5B^2}$$

9. countonme123

yah thats right i get it thanks

10. AccessDenied

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. :)