Question:
How many identities are there for Algebraic Expressions
Answer:
An algebraic identity is an equality that holds for any values of its variables.
Ex: The identity
(a + b)2 = a2 + b2 + 2ab
holds for all values of a and b.
There are some important algebraic identities are:
1. (a + b)2 = a2 + b2 + 2ab
Ex: (101)2 = (100 + 1)2 = (100)2 + 12 + 2 * 100 * 1 = 10000 + 1 + 200 = 10201
2. (a - b)2 = a2 + b2 - 2ab
Ex: (99)2 = (100 - 1)2 = (100)2 + 12 - 2 * 100 * 1 = 10000 + 1 - 200 = 10001 - 200 = 9801
3. a2 - b2 = (a - b)*(a + b)
Ex: (x2 - 25) = x2 - 52 = (x - 5)*(x + 5)
4. (x + a)*(x + b) = x2 + (a + b)x + ab
Ex: (x + 5)*(x + 2) = x2 + (5 + 2)x + 5*2 = x2 + 7x + 10
5. (x - a)*(x - b) = x2 - (a + b)x + ab
Ex: (x - 5)*(x - 2) = x2 - (5 + 2)x + 5*2 = x2 - 7x + 10
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