SOLUTION: Factor By Grouping 2x^2+6xy-5xy-15y^2 Please show and explain steps on how to factor this by grouping. Thanks so much!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor By Grouping 2x^2+6xy-5xy-15y^2 Please show and explain steps on how to factor this by grouping. Thanks so much!      Log On


   

Question 612938: Factor By Grouping
2x^2+6xy-5xy-15y^2
Please show and explain steps on how to factor this by grouping. Thanks so much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2%2B6xy-5xy-15y%5E2 Start with the given expression


%282x%5E2%2B6xy%29%2B%28-5xy-15y%5E2%29 Group the terms in two pairs


2x%28x%2B3y%29-5y%28x%2B3y%29 Factor out the GCF 2x out of the first group. Factor out the GCF -5y out of the second group


%282x-5y%29%28x%2B3y%29 Since we have the common term x%2B3y, we can combine like terms


So 2x%5E2%2B6xy-5xy-15y%5E2 factors to %282x-5y%29%28x%2B3y%29


In other words, 2x%5E2%2B6xy-5xy-15y%5E2=%282x-5y%29%28x%2B3y%29 for all values of x and y.