How do you go about factorising this simply and easily?
I arrived at the correct answer (x - y)(2x + 3y) only after thinking and playing around with it for ages.
It's been a long time since I went over this in class.
Find the product of the coefficients of x^2 and y^2 which in this case is -6. Now find such pair of factors of -6 so that their sum is the coefficient of middle term, in this case 1. -6 = 2 * -3; -6 = -2 * 3 and so on. we observe that the sum of 3 + ( -2 ) is 1 so we split the middle term and re write the expression
2x2 + xy - 3y2= 2x^2 + 3xy-2xy-3y^2 = x(2x +3y) -y(2x+3y) Etc.....