Factoring Difference of Squares a2 – b2

Perfect Squares The product of a rational number multiplied by itself. What are they? The product of a rational number multiplied by itself.

You may add the perfect squares to your multiplication chart. 12 = 22 = 32 = 42 = 52 = 62 = 1 72 = 82 = 92 = 102 = 112 = 122 = 49 There are an infinite number of perfect squares. However, we only need to be familiar with the first 12. 4 64 9 81 100 16 25 121 144 36

In order to use difference of squares: You must have a subtraction problem Every part of the problem must be a square.

Steps to Factoring Difference of Squares Factor GCF (if needed) 2. Draw parenthesis ( )( ) 3. Put a plus sign in one, a subtraction sign in the other. ( + )( - ) 4. Put the first squared term in front. (a + )(a - ) a2 – b2 = Put the second squared term in back. (a + b)(a - b) *It does not matter the order!

You can always check your answer by using F.O.I.L.

Factor each polynomial if possible Factor each polynomial if possible. If the polynomial cannot be factored, write prime. Ex. 1 x2 – 4 Ex. 2 81 – r2

Factor each polynomial if possible Factor each polynomial if possible. If the polynomial cannot be factored, write prime. Ex. 3 4x2 - 16 Ex. 4 144x2 – 9y2

Factor each polynomial if possible. Ex. 5 36x2 – 9 Ex. 6 25x2 – 49y2

Factor each polynomial if possible. Ex. 7 144n2 – 121m2