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?

To factor the difference of two squares I will use y^2 - 9 To factor this the first term is broken up in the following format: (y - ?) (y + ?) The second term is broken up into its rooted number. (? – 2) (? + 9) When combined the terms look like this (y – 2) (y + 9) A problem for the class to solve is: x^2 – 4 To factor a perfect square trinomial I will use y^2 + 10y + 25 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 5 and 5 are factors of 25 and add up to 10. y^2 + 5y +5y + 25 We then group the first two terms and the last two terms. (y^2 + 5y) ( 5y + 25) Then factor the GCF out of each grouping. y( y+ 5) 4 (y+5) We are left with (y + 5) (y + 5) A problem for the class to solve is x^2 + 10x + 25 To factor the difference of two cubes I will use (y^3 – 64) (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, y and the 3rd root of the second term, 5. This end up looking like this: (y – 4) (y^2 + 4y +16) A problem for the class to solve is (x^3 – 27)