Demonstrate how to factor the difference of two squares, a perfect square trinomial, and the sum and difference of two cubes. Which of these three makes the most sense to you? Give a problem for the class to factor.

To factor the difference of two squares I will use x^2 - 4 To factor this the first term is broken up in the following format: (x - ?) (x + ?) The second term is broken up into its rooted number. (? – 2) (? + 2) When combined the terms look like this (x – 2) (x + 2) A problem for the class to solve is: x^2 – 9 To factor a perfect square trinomial I will use x^2 + 8x + 16 To break the trinomial up into groupable terms you must multiply the a and the c terms and see what factors add up to the b term. In this case 4 and 4 are factors of 16 and add up to 8. x^2 + 4x +4x + 16 We then group the first two terms and the last two terms. (x^2 + 4x) ( 4x + 16) Then factor the GCF out of each grouping. x( x + 4) 4 (x+4) We are left with (x + 4) (x + 4) A problem for the class to solve is x^2 + 10x + 25 To factor the difference of two cubes I will use (x^3 – 125) (a^3 – b^3) To break up this cubes you must use the following format: (a – b)(a^2 + ab + b^2) In our example problem we will plug in our 3rd root of the first term, x and the 3rd root of the second term, 5. This end up looking like this: (x – 5) (x^2 + 5x +25) A problem for the class to solve is (x^3 – 8)