Last post I discussed common factor, which we will be using in concert with difference of squares. Difference of squares factors x2<\/span><\/sup> – 36 into (x + 6)(x – 6). By the foil<\/a> method you can confirm:<\/p>\n F: x*x=x2<\/span><\/sup><\/p>\n O: x*-6=-6x<\/p>\n I: 6*x=6x<\/p>\n L: 6*-6=-36<\/p>\n Displaying the terms in a row we get<\/p>\n x2<\/span><\/sup> – 6x + 6x – 36 = x2<\/span><\/sup> – 36<\/p>\n Example: Factor x2<\/span><\/sup> – 49<\/strong><\/p>\n Solution: We notice that the square root of 49 is 7. Therefore we write<\/p>\n x2<\/span><\/sup> – 49 = (x + 7)(x – 7)<\/p>\n Difference of squares is easy to spot and factor if it’s plain. However, it may be “hidden” by a common factor:<\/p>\n Example: Factor 2x3<\/span><\/sup> – 50x<\/strong><\/p>\n Solution: We notice that 50x isn’t square rootable. However, we also notice that 2x can be taken out front as a common factor<\/a>:<\/p>\n 2x3<\/span><\/sup> – 50x = 2x(x2<\/span><\/sup> – 25)<\/p>\n Now, we’re getting somewhere: we follow with<\/p>\n 2x(x2<\/span><\/sup> – 25) = 2x(x + 5)(x – 5)<\/p>\n Removing the common factor of 2x allowed us to apply the difference of squares technique.<\/p>\n Have a nice day:)<\/p>\n