3a^2/4+2ab/3+ab-a^2

Question

3a^2/4+2ab/3+ab-a^2

fibonaccichick666 · Answer

What would you like to do?

anonymous · Answer

Simplify the equation.

fibonaccichick666 · Answer

ok, so we have $$\frac{3a^2}{4}+\frac{2ab}{3}+ab-a^2$$ carrect?

anonymous · Answer

Yes.

fibonaccichick666 · Answer

So, first, can you tell me what the like terms are?

anonymous · Answer

3a^2 & -a^2, 2ab & ab.

fibonaccichick666 · Answer

ok, now you left out the denominators of the coefficients, was that intentional?

anonymous · Answer

No.

fibonaccichick666 · Answer

ok, so I think that is where your problem is.  You did very well at identifying the like terms, but you cannot forget the denominators in this case.  Since multiplication is commutative, you can write 3a^2/4 a few different ways.  $$\frac{3a^2}{4}=\frac{3}{4}a^2=\frac{1}{4}3a^2=3\frac{a^2}{4}$$

fibonaccichick666 · Answer

those are all equivalent statements, so when you combine your like erms, you have to remember the whole coefficient, not just the numerator

fibonaccichick666 · Answer

also(there should be parentheses around one of those to show multiplication up ther like this ) $$(\frac{3a^2}{4})=(\frac{3}{4})a^2=(\frac{1}{4})3a^2=3(\frac{a^2}{4})$$

anonymous · Answer

Ok.

fibonaccichick666 · Answer

so, can you combine your like terms for me  now?

anonymous · Answer

If I combine like terms, would my equation then be: 2a^2/4+3ab/3?

fibonaccichick666 · Answer

well, how did you combine the 3a^2/4 & -a^2?

anonymous · Answer

I have no idea, I'm extremely confused.

fibonaccichick666 · Answer

ok, so if you had $\frac{3}{4}+(-1)$ what would you do?

anonymous · Answer

-1/4

fibonaccichick666 · Answer

good! so it is the exact same here

fibonaccichick666 · Answer

ACTUALLY, a really cool thing $$\frac{3a^2}{4}-a^2=(\frac{3}{4}-1)a^2$$ It is called the distributive property

anonymous · Answer

That makes sense!

fibonaccichick666 · Answer

yup yup, so now, can you combine the ab terms?

anonymous · Answer

(2ab/3+ab)= (2/3+1)ab?

fibonaccichick666 · Answer

yep

fibonaccichick666 · Answer

once you hit a certain level, we tend to forget when we explain that this is really what we are doing.  We skip steps so much that we forget they exist

anonymous · Answer

Thanks for your help, it was greatly appreciated!

fibonaccichick666 · Answer

np, just remember it is the commutativity of addition and the distributive property that allows you to do these things like grouping your like  terms and factoring

fibonaccichick666 · Answer

medal pwease?