factor by grouping.
12x^2-9xy-8xy+6y^2

Question

factor by grouping.
12x^2-9xy-8xy+6y^2

mathmale · Answer

Julie:  How have you applied factoring by grouping in the past?

Note how the first two terms both contain x and that the last two terms both contain y.  
This suggests that x can be factored out of the first two terms and y out of the last two terms:  x(12x - 9y) - y(8x - 6y). 

Now look at that (12x - 9y) and (8x - 6y).  See any pattern?  See anything in common to both?

Note how (12x - 9y) = 3(4x - 3y) and (8x - 6y) = 2(4x - 3y).  See anything / any factor common to both?  

Hope this helps you get started at factoring 12x^2-9xy-8xy+6y^2 by grouping.  Please give it a try on your own.  Further questions?  Just ask.

anonymous · Answer

is (12x^2+6y^2)(-9xy-8xy) right

mathmale · Answer

You could check your answer by multiplying your two factors together.

mathmale · Answer

Let's go back to x(12x - 9y) - y(8x - 6y).  
Inside the first set of parentheses is 12x - 9y.  Do these terms have anything in common?  If there's a common factor, please factor it out.
Inside the second set of parentheses is 8x - 6y.  Do these terms have anything in common?  If there's a common factor, please factor it out.

anonymous · Answer

3x-3y & 2y-3?

mathmale · Answer

Let's go back to x(12x - 9y) - y(8x - 6y).  Would you agree that, after factoring, this expression becomes 3x(4x - 3y) - 2y(4x - 3y)?  Again, I ask you to look for any term or factor that shows up more than once and thus is a common factor.

After factoring,  3x(4x - 3y) - 2y(4x - 3y) becomes (4x - 3y)*( what? )

anonymous · Answer

12x^2-9xy

mathmale · Answer

Julie, it appears that you are MULTIPLYING where you should be doing the opposite:  factoring.  You've multiplied 3x*(4x - 3y).

Instead, please look at 3x(4x - 3y) - 2y(4x - 3y) again and verify the following:

(4x - 3y) is the factor common to both the left and the right term of this expression.

Factoring (4x - 3y) out, we are left with (3x - 2y).

Thus, 3x(4x - 3y) - 2y(4x - 3y) factors into (4x - 3y)(3x - 2y).  

Check by multiplying this out.

anonymous · Answer

thanks

mathmale · Answer

You're welcome!  Hope you can successfully apply these principles to other factoring by grouping problems.