Simplifying Polynomials Helpp!!

AJ22

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Sep 21, 2021
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3xy(4x^2 + 3x) - 5x^2(2xy - 3y) / 4x

I have tried using distributive property and then dividing by 4x but it does't seem to make sense. I get an answer of 6xy + x^2y/2...
Any help would be greatly appreciated. The entire thing is being divided by 4x in the question.
 

Otis

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Apr 22, 2015
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3xy(4x^2 + 3x) - 5x^2(2xy - 3y) / 4x

The entire thing is being divided by 4x in the question
Hi AJ. When texting, we show numerators and denominators by putting grouping symbols around them (except when they're a single number). Like this:

(3xy(4x^2 + 3x) - 5x^2(2xy - 3y))/(4x)

I get an answer of 6xy + x^2y/2
[imath]6xy + \frac{x^2y}{2}[/imath]

EDIT: Yes, that's correct. (I'd dropped an x in my previous attempt.)

If it looks strange, you could write the factor 1/2 in front (a coefficient)

[imath]6xy + \frac{1}{2}x^2y[/imath]

😎
 

AJ22

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Sep 21, 2021
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Hi Otis, Thanks for the response, would there be any factoring involved before dividing by 4x. If thats the case I seem to get an answer of [x(x+12)[/2]
 

Otis

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Apr 22, 2015
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Oops -- I'm the one that messed up the multiplications. Your previous answer is correct, too. Please excuse me (or Jomo will send me to the corner).

would there be any factoring involved before dividing by 4x. If thats the case I seem to get an answer of [x(x+12)[/2]
You meant to type the y also, yes? With the grouping symbols fixed, that's a factored form of the simplification.

[xy(x+12)]/[2]

Were I to write that, I would express dividing by two as multiplying by 1/2.

1/2(xy)(x + 12)

Good job simplifying, with both results.

:)
 

Otis

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Apr 22, 2015
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3,808
would there be any factoring involved before dividing by 4x.
I wouldn't think so. You probably want the simplified polynomial in your first post as the answer.

6xy + (1/2)(x^2y)

But, whether we were going for that polynomial form or a factored version of it, I still believe that distributing and combining like-terms in the numerator first (as you did) is the way to go.

My initial goofed-up claim probably threw you off.

😎
 
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