|
|
Line 12: |
Line 12: |
|
| |
|
| <math>= x^2+6x+9</math> | | <math>= x^2+6x+9</math> |
| | |
|
| |
|
| Example 2: Factorise <math>49a^2+70ab+25b^2</math> | | Example 2: Factorise <math>49a^2+70ab+25b^2</math> |
Line 19: |
Line 20: |
| <math>(7a)^2+2(7)(5)ab+(5b)^2</math> | | <math>(7a)^2+2(7)(5)ab+(5b)^2</math> |
|
| |
|
| using the identity 1 <math>a=7a , b = 5b</math> | | using the identity I <math>a=7a , b = 5b</math> |
|
| |
|
| <math>49a^2+70ab+25b^2 = (7a+5b)^2 = (7a+5b)(7a+5b)</math> | | <math>49a^2+70ab+25b^2 = (7a+5b)^2 = (7a+5b)(7a+5b)</math> |
Line 28: |
Line 29: |
| === Identity III === | | === Identity III === |
| <math>a^2-b^2=(a+b)(a-b)</math> | | <math>a^2-b^2=(a+b)(a-b)</math> |
| | |
| | Example: <math>\frac{49}{4}x^2 - \frac{y^2}{9}</math> |
| | |
| | <math>\left [ \frac{7x}{2} \right ]^2 -\left [ \frac{y}{3} \right ]^2</math> |
| | |
| | Using the identity III |
| | |
| | <math>\frac{49}{4}x^2 - \frac{y^2}{9}</math> |
|
| |
|
| === Identity IV === | | === Identity IV === |
Revision as of 13:37, 5 March 2024
The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are used for the factorization of polynomials. Algebraic identities are used in the computation of algebraic expressions and solving different polynomials.
Algebraic Identities
Some Standard Algebraic Identities list are given below:
Identity I
Example 1: Evaluate using the identities
Example 2: Factorise
, ,
using the identity I
Identity II
Identity III
Example:
Using the identity III
Identity IV
Example: Evaluate using the identities
Identity V
Identity VI
Identity VII
Identity VIII