6x^2-4xy-15xy+10y^2 factor by grouping

4 answers · Mathematics

Best Answer

We will need to split the middle term and use the grouping method. To do this multiply the coefficient of the first term (6) against the coefficient of the last term (10):

6 * 10 = 60

Factors of 60 = + - (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)

From the list of factors find two numbers that when added together give - 19 and when multiplied together give 60. - 15 and - 4 added together give - 19 and multiplied together give 60 so split the middle term by rewriting these values back into the expression:

6x^2 - 15xy - 4xy + 10y^2

Now use the grouping method, take out the highest common factor between the two sets of terms:

3x (2x - 5y) - 2y (2x - 5y)

Group the outside terms:

(3x - 2y) (2x - 5y)

Answers

6 = - 3*-2

10 = 5*2

5*3+2*2=19

thus

(2y-3x) (5y-2x)