How Standard Algebraic Identities are in Real Life Situations

The algebraic identities are the equations in which LHS and RHS stand equal, irrespective of the value of the Variables used. Algebraic identities are a vital concept of mathematics because of their real-life implications. The uses of algebraic identities are primarily done in various other mathematics concepts. 

There are mainly two types of algebraic identities derived from the binomial theorem, i.e., binomial and trinomial. This article deals with the definition of algebraic identities, the types of Algebraic identities, and the uses of algebraic identities in real life.

What is the definition of Algebraic Identities?

An equality relation, which stands true irrespective of the variable’s value put in the equation, is called an identity. 

The definition of Algebraic Identities is that the algebraic equations that stand equal irrespective of the variable’s value are known as Algebraic Identities. Simplifying and restructuring the complex algebraic equations is done by Identities. 

What is Binomial expansion? 

A Binomial expansion is a theorem that states the expansion of two variables with a sum of n degrees. All the standard identities are derived from Binomial theorems. 

What are the types of Algebraic identities? 

Algebraic identities are the standard identities derived from the multiplication of binomials. 

There are several types of algebraic identities. 

The most important types of algebraic identities are binomial algebraic identities and trinomial Algebraic Identities. 

Binomial algebraic identities are derived from binomials consisting of a sum of two-term powers. In comparison, trinomial algebraic identities derived from binomials consist of a sum of three-term power. 

The main algebraic identities are as follows-

1. (a+b)²=a²+2ab+b²

2. (a–b)²=a²–2ab+b²

3. (a+b)(a–b)=a²–b²

4. (x+a)(x+b)=x²+(a+b)x+ab

The Other important identities are as follows;

1.  (a+b+c)²=a²+b²+c²+2ab+2bc+2ac

2. (a+b)³=a³+b³+3ab(a+b)

3. (a–b)³=a³–b³–3ab(a–b)

4. (a+b+c)(a²+b²+c²–ab–bc–ca)=a³+b³+c³–3abc

5. (a + b) (a + c) (b + c) = (a + b + c) (ab + ac + bc) – abc

6. a² + b² + c²= (a + b + c)² – 2(ab + ac + bc)

7. a³+b³+c³–3abc=(a+b+c)(a²+b²+c²–ab–bc–ca)

8. (a–b)(a–c)=a²– (b+c)a+bc

How do we prove different types of Algebraic identities? 

Algebraic Identities are Standard Identities. They are derived from Binomial theorems. To prove these theorems, it is required to prove LHS is equal to RHS. 

So, for example, to prove the Algebraic Identity –

(a+b)²=a²+2ab+b²

Taking, LHS = (a+b)²

L.H.S. = (a + b) (a + b)

               a² + ab + ab + b²

L.H.S. = a² + 2ab+b²

Hence, proved: L.H.S. = R.H.S.

What are the uses of algebraic identities in real life?

To find an area of a rectangular piece of land whose length and breadth are 993 m and 889 m without a calculator or a mobile phone is a difficult task. How to find the answer to this complex equation? The answer can be found by using algebraic identities.

In this equation, the area of the rectangle = length × breadth. 

 = 993×889

= (1000-7) (1000-111)

Using identity (a – b) (a – c) = a² – (b + c)a + bc

1000 2 – (7+111)1000+7×111

= 1000000 – 118000+777

= 882777 m²

And that’s the area of the rectangular plot of land. Algebra Identities are considered to be a crucial Mathematical concept. It is not only used to calculate complex algebraic equations and polynomials, but it also has real-life implications. Algebraic identities are used in advanced mathematical concepts such as integration and differentiation. The use of algebraic identities in real life can be seen in various instances of our life. It makes the calculations very simple and easy. 

Conclusion 

The definition of Algebraic identities is the algebraic equations that stand equal irrespective of the variable’s value. 

Algebraic identities are the standard identities that are used to simplify complex equations. 

The two types of algebraic identities are Binomial and trinomial Algebraic Identities. 

These identities are used in real life. From calculating how many boxes, tons of raw material will fit into calculating the area of your room. 

These are used as algebraic identities all the time. These real-life implications make the algebraic identities much more vital.