Multiplying Binomials Using Alge-Tiles

Multiplying Binomials Algebraically : FOIL

Special Cases

A special product is a type of multiplication question where a repetitive pattern in the calculation allows us to learn SHORT CUTS! 

Types of special products                    Ex1. Expand and Simplify (a + 5)2
·         Perfect squares                          Rewrite as (a + 5) (a + 5)                  
·         Difference of squares                                = a2 + 5a + 5a + 25           
Ex2. Expand and Simplify (a + 3) (a – 3)         = a2 + 10a + 25
                       = a2 – 3a + 3a – 9 
                       = a2 – 9 

Perfect squares                            
Short cut:
1.      Square the first term.
2.      Multiply the two terms together and double the result.
3.      Square the second term.
Ex. (2a + 2)2
            = 4a2 + 8a + 4 

Difference of square
Short cut:
1.      Square the first term
2.      Place a (–) sign
3.      Square the second term
Ex. (3k + 8) (3k – 8)
              = 9k2 – 64