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(**) Difference Of Two Squares  (a² – b²):

   A.  This method is often used in two different ways but each way is very easy to learn.  Both ways use the following rule from algebra:

a² – b² = (a + b) (a – b)

   B.  The first way is using the form: (a² – b²).

1.  Add the two numbers together.

2.  Subtract the right number from the left number.

3.  Multiply these two values together for the answer.

Ex [1]  29² – 21² =_________.

a)      29 + 21 = 50.

b)      29 – 21 = 8.

c)      8 x 50 = 400.

d)      The answer is 400.

 Ex [2]  12² – 88² =_________.

a)      12 + 88 = 100.

b)      12 – 88 = -76.

c)      -76 x 100 = -7600.

d)      The answer is -7600.

   C.  Sometimes you see two numbers multiplied together that are in this form : (a + b) (a – b).  Two numbers in this form can be difficult to recognize so look carefully before deciding what method to use.

1.  If you see numbers in this form simply use a² – b².

Ex [1]  (40 + 3) (40 – 3) =_________.

a)      40² – 3² = 1600 – 9 = 1591.

b)      The answer is 1591.

Ex [2]  19 x 21 =_________.

a)      Think of this as being (20 – 1) x (20 + 1).

b)      20² – 1² = 400 – 1 = 399.

c)      The answer is 399.

Ex [3]  13 x 19 =_________.

a)      Think of this as being (16 – 3) x (16 + 3).

b)      16² – 3² = 256 – 9 = 247.

c)      The answer is 247.

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