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# Perfom the indicated operation and simplify?

I'm trying to multiply rational expressions with two variables and I'm getting confused. I know I need to factor, but my mind just hates variables. Anyways, the problem is:

x2+xy-2y^2 over 4y * x+2y over 12y^2. Please show all steps. Thank you!

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- StevenLv 78 years agoFavorite Answer
x2+xy-2y^2 over 4y * x+2y over 12y^2.

(x2+xy-2y^2)/4y * (x+2y)/12y^2.

multiply the numerators

(x2+xy-2y^2)*(x+2y)

distribute

x(x2+xy-2y^2)+2y(x2+xy-2y^2)

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

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

(x^3+3x^2y-4y^3)

the numerators

4y(12y^2)

48y^3

all together

(x^3+3x^2y-4y^3)/48y^3

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