what are the four algebraic identities.
with examples
1.
(a + b)2 = a2 + 2ab + b2
For example,
(200 + 8)2
= (200)2 + 2 (200) (8) + (8)2
= 40000 + 3200 + 64
= 43264
2.
( a- b )2 = a2 - 2ab + b2
For example,
(100 − 1)2 = (100)2 − 2 (100) (1) + (1)2
= 10000 − 200 + 1
= 9800 + 1
= 9801
3.
( a + b) (a - b) = a2 - b2
For example,
(15 + 10)(15 - 10) = 152 - 102
= 225 - 100 = 125
4.
(x + a) ( x + b) = x2 + (a + b) x + ab
For example,
102 × 105 is written as: (100 + 2) (100 + 5)
So, (100 + 2) (100 + 5) = (100)2 + (2 + 5) × 100 + 2 × 5
= 10000 + 700 + 10
= 10710
