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Example:Solve using Algebraic Identity

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In mathematics, a polynomial (from Greek poly, "many" and medieval Latin binomium, "binomial" is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x2 − 4x + 7 is a polynomial, but x2 − 4/x + 7x3/2 is not, because its second term involves division by the variable x (4/x) and because its third term contains an exponent that is not a whole number (3/2).




Sum/difference of two squares


A visual illustration of the identity (a + b) 2 = a2 + 2ab + b2 (Our solved example in mathguru.com uses this concept)

Another common type of algebraic factoring is called the difference of two squares. It is the application of the formula

to any two terms, whether or not they are perfect squares. If the two terms are subtracted, simply apply the formula. If they are added, the two binomials obtained from the factoring will each have an imaginary term. This formula can be represented as

For example, 4x2 + 49 can be factored into (2x + 7i) (2x − 7i).


Factoring other polynomials

Sum/difference of two cubes

Another formula for factoring is the sum or difference of two cubes. The sum can be represented by

and the difference by

For example, x3 − 103 (or x3 − 1000) can be factored into (x − 10) (x2 + 10x + 100). (Our solved example in mathguru.com uses this concept)




The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.