Question

please tell the four important identities​

Answer 1

Answer:

The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are also used for the factorization of polynomials. In this way, algebraic identities are used in the computation of algebraic expressions and solving different polynomials. You have already learned about a few of them in the junior grades. In this article, we will recall them and introduce you to some more standard algebraic identities, along with examples

Step-by-step explanation:

Standard Algebraic Identities List

All the standard Algebraic Identities are derived from the Binomial Theorem, which is given as:

(a+b)n=nC0.an.b0+nC1.an−1.b1+……..+nCn−1.a1.bn−1+nCn.a0.bn

Some Standard Algebraic Identities list are given below:

Identity I: (a + b)2 = a2 + 2ab + b2

Identity II: (a – b)2 = a2 – 2ab + b2

Identity III: a2 – b2= (a + b)(a – b)

Identity IV: (x + a)(x + b) = x2 + (a + b) x + ab

Identity V: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

Identity VI: (a + b)3 = a3 + b3 + 3ab (a + b)

Identity VII: (a – b)3 = a3 – b3 – 3ab (a – b)

Identity VIII: a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)

 

Answer 2

Identity - [i]

$\sf {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

Identity - [ii]

$\sf {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

Identity - [iii]

$\sf(x + y)(x - y) = {x}^{2} - {y}^{2}$

Identity - [iv]

$\sf(x + a)(x + b) = {x}^{2} + x(a + b) + ab$