How to Factor the Foil , Difference of Two Squares ?

Question

campbell_st · Answer

basically find the factors of the constant term that add to the coefficient of the middle term

e.g. x^2 + 8x + 15 = 0                  factors of 15    that add to 8

                                                                   1 + 15 = 16
                                                                     3 + 5   = 8

the factors are 3 and 5
so the quadratic can be factorised to (x + 5)(x + 3)= 0

same for 

x^2 - 11x -26 = 0                 you want the factors of -26 that add to -11

The hint here is that because the value of middle term is      -11  the larger factor is negative

                    -26 + 1 = -25
                     -13 + 2 = -11

so the factors are -13, 2

(x -13)(x +2)=0

difference of 2 squares is easier... there are only 2 terms.... both are squares with a negative between them. Take the square root of each... the constant will have  a positive and negative value

e.g. x^2 - 4 = 0       (x - 2)(x +2) = 0

       x^2 - 49 = 0     (x - 7)(x+7) =0

hope it helps