Explore Related Concepts


Algebraic Identities
 (a + b )^{2} = a^{2} + 2ab + b^{2}
 (a  b )^{2} = a^{2} 2ab + b^{2}
 (a + b ) ( a  b ) = a^{2}  b^{2}
Best Results From Wikipedia Yahoo Answers Youtube
From Wikipedia
In mathematics, the term identity has several different important meanings:
 An identity is a relation which is tautologically true. This is usually taken to mean something that is true by definition, either directly by the definition, or as a consequence of it. For example, algebraically, this occurs if an equation is satisfied for all values of the involved variables. Definitions are often indicated by the 'triple bar' symbol â‰¡, such as A^{2}â‰¡ xÂ·x. The symbol â‰¡ can also be used with other meanings, but these can usually be interpreted in some way as a definition, or something which is otherwisetautologically true (for example, a congruence relation).
 In algebra, an identity or identity elementof a set S with abinary operationÂ· is an element e that, when combined with any element x of S, produces that same x. That is, for all x in S. An example of this is the identity matrix.
 The identity functionfrom a set S to itself, often denoted \mathrm{id} or \mathrm{id}_S, is the function which maps every element to itself. In other words, \mathrm{id}(x) = x for all x in S. This function serves as the identity element in the set of all functions from S to itself with respect to function composition.
Examples
Identity relation
A common example of the first meaning is the trigonometric identity
 \sin ^2 \theta + \cos ^2 \theta = 1\,
which is true for all complex values of \theta (since the complex numbers \Bbb{C} are the domain of sin and cos), as opposed to
 \cos \theta = 1,\,
which is true only for some values of \theta, not all. For example, the latter equation is true when \theta = 0,\, false when \theta = 2\,.
See also list of mathematical identities.
Identity element
The concepts of "additive identity" and "multiplicative identity" are central to the Peano axioms. The number 0 is the "additive identity" for integers, real numbers, and complex numbers. For the real numbers, for all a\in\Bbb{R},
 0 + a = a,\,
 a + 0 = a,\, and
 0 + 0 = 0.\,
Similarly, The number 1 is the "multiplicative identity" for integers, real numbers, and complex numbers. For the real numbers, for all a\in\Bbb{R},
 1 \times a = a,\,
 a \times 1 = a,\, and
 1 \times 1 = 1.\,
Identity function
A common example of an identity function is the identity permutation, which sends each element of the set \{ 1, 2, \ldots, n \} to itself or \{a_1,a_2, \ldots, a_n \} to itself in natural order.
Comparison
These meanings are not mutually exclusive; for instance, the identity permutation is the identity element in the group of permutations of \{ 1, 2, \ldots, n \} under composition.
From Yahoo Answers
Answers:When the identity symbol of three lines is used it means that the two sides are equal for every value of the variable. Another way of expressing this is that there must be the same number of x's on both sides, the same number of x^2's etc. So x^2  ax + 144 = (x  b)^2 = x^2  2bx + b^2 The x^2's are already equal but also 144 = b^2 > b = 12 or 12 ax = 2bx > a = 2b So either x^2  24x + 144 = (x  12)^2 or x^2 + 24x + 144 = (x + 12)^2 Edit. b^2 = 144 > b = +/sqrt(144) = +/12 As you said, it's because 12 is square root of 144. That's all there is to it!
Answers:(x + 1)/x = 4 x + 1 = 4x x  4x = 1 3x = 1 x = 1/3 x = 1/3 (x^3 + 1)/x^3 = x^3/x^3 + 1/x^3 = 1 + 1/(1/3)^3 = 1 + 1(3/1)^3 = 1 + 27 = 28
Answers:Algebraic identities are just algebraic expressions we know are equivalent. For example: x + x = 2x is true in any algebraic structure that contains whole numbers and includes the distributivity law for multiplication and addition. That's an identity, because it doesn't matter what x is, it's always true. You can make algebraic identities very long if you want to, but generally, length of an identity is inversely proportional to how interesting and relevant it is.
Answers:This site answers most of these questions, and gives you the idea how to do the others. It's very difficult to explain in words. http://library.thinkquest.org/C0110248/algebra/alidentities.htm
From Youtube