In this article, we collect the most practical examples of notable identities , as well as their functions, to help you understand this interesting topic at a higher level.
What are notable identities?
Remarkable identities can be defined as products or multiplications that can be reflected algebraically, fulfilling established and permanent rules. Each notable identity belongs to a factoring formula.
These have the purpose of solving an algebraic expression without requiring to verify the product since by using the factoring formula, you simplify the complexity of the expressions.
These are composed of binomials or the result of two binomials, to be able to execute them correctly you will only need to memorize the formulas that it has, since knowing them will make it easier for you to solve the notable identities.
What is factoring?
This consists of the decomposition of a polynomial into two or more factors, so that if these are multiplied, it results in the initial figure. You could also say that it is the transformation of an algebraic sum into factors.
This process is very different from multiplication, since factorization does not have detailed rules, it is executed according to the practice obtained and its objective is to reflect the polynomial in a combination of factors.
Notable product examples
Now, we will give you a list of the best examples of notable identities , so that you know it and learn to use them in a simpler way
- The common factor.
- The square of a binomial
- Lagrange identities
- The square of a polynomial
- Legendre’s identities
- The cube of a binomial
- The product of binomials with common term
- Argand’s identity
- The product of two conjugated binomials.
After providing you with a series of examples about notable identities, we will also provide you with examples of notable identities through algebraic expressions, so that you can understand their effect at a higher level:
- (a + b) 2 = a2 + 2 a b + b2
- (a – b) 2 = a2 – 2 a b + b2
- (a + b) · (a – b) = a2− b2
- (a + b) 3 = a3 + 3 a2 b + 3 a b2 + b3
- (a – b) 3 = a3 – 3 a2 b + 3 a b2 – b3
- (a + b + c) 2 = a2 + b2 + c2 + 2 a b + 2 a c + 2 b c
- a3 + b3 = (a + b) · (a2 – ab + b2)
- a3− b3 = (a – b) · (a2 + ab + b2)
- (x + a). (x + b) = x2 + (a + b) x + ab
- (a + b) 2+ (a – b) 2 = 2. (a2 + b2)
- (x2 + x + 1). (x2 – x + 1) = x4 + x2 + 1
- (a + b) = c. a + c. b
- (a + b) 3 = a3 + 3a2.b + 3ab2 + b3
Remarkable identities are by far essential in algebraic mathematics, because as we could observe in the previous paragraphs, it facilitates us at great levels the resolution of algebraic expressions and mathematical problems regardless of whether they are complex or simple, we hope that our article has you been helpful.