# SOLUTION: Please factorise the following(Please do not use the quadratic formula) 12x squared +17xy-5y squared Thank you

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 Question 359147: Please factorise the following(Please do not use the quadratic formula) 12x squared +17xy-5y squared Thank youAnswer by Edwin McCravy(9717)   (Show Source): You can put this solution on YOUR website!```Factorise: 12x² + 17xy - 5y² Multiply the 12 by 5, disregarding the sign, getting 60. Write down a list of all the ways to factorise 60 using two positive integers: 60*1 = 60 30*2 = 60 20*3 = 60 15*4 = 60 12*5 = 60 10*6 = 60 Now look at the sign of the last term to see whether we add or subtract those pairs of numbers. The last term is -5y², which has a - sign, so we subtract those same pairs of numbers that we multiplied above to get 60. (when the last term has a + sign, we add, but since it has a -, we subtract): 60-1 = 59 30-2 = 28 20-3 = 17 15-4 = 11 12-5 = 7 10-6 = 4 And we look down that list to find the coefficient of the middle term of 12x² + 17xy - 5y², in absolute value, which is 17 and we find it as 20-3 = 17 So we substitute (20-3) in place of 17 12x² + 17xy - 5y² 12x² + (20-3)xy - 5y² and remove the parentheses: 12x² + 20xy - 3xy - 5y² Next we factorise only the FIRST two terms by factorising out 4x: 4x(3x + 5y) - 3xy - 5y² Next we factorise only the LAST two terms by factorising out -y: 4x(3x + 5y) - y(3x + 5y) Notice that the two parentheses are the same. I'll colour them red: 4x(3x + 5y) - y(3x + 5y) So factorise out the red factor, leaving the black terms in parentheses: (3x + 5y)(4x - y) Edwin```