## countonme123 Group Title help with polynomials? 2 years ago 2 years ago

1. countonme123 Group Title

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

2. alexwee123 Group Title

hunger games :D

3. countonme123 Group Title

:)

4. countonme123 Group Title

can you guys help me

5. AccessDenied Group Title

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

6. AccessDenied Group Title

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 Group Title

it helps a bit

8. AccessDenied Group Title

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 Group Title

yah thats right i get it thanks

10. AccessDenied Group Title

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. :)