Simplify
6x^2y + 9xy^2 - 18x^3 over
3х
2y + 3xy - 6x^2
Show the steps
We can simplify the expression by factoring out 3x from each term in the numerator:
6x^2y + 9xy^2 - 18x^3 = 3x(2x^2y + 3y^2 - 6x^2)
Now we can divide both terms in the numerator and denominator by 3x:
(3x(2x^2y + 3y^2 - 6x^2)) / (3x) = 2x^2y + 3y^2 - 6x^2
And we can rearrange the terms to put the variable with the highest exponent first:
-6x^2 + 2x^2y + 3y^2 = -6x^2 + 2xy^2 + 3y^2x
Now we can factor out the common factor of xy from the last two terms:
-6x^2 + 2xy(y + 3x)
Finally, we can write the simplified expression:
(6x^2y + 9xy^2 - 18x^3) / (3х) = -2x(3x - y)(y + 3x) / (3x) = -2(3x - y)(y + 3x)
To simplify the expression (6x^2y + 9xy^2 - 18x^3)/(3x), you can start by factoring out the common terms.
First, let's factor out the common factor in the numerator, which is 3x:
3x(2xy + 3y^2 - 6x^2)/(3x)
Next, cancel out the common term 3x in the numerator and the denominator:
(2xy + 3y^2 - 6x^2)/1
Therefore, the simplified expression is 2xy + 3y^2 - 6x^2.