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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