Difference between revisions of "Algebraic Identities"
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Some Standard Algebraic Identities list are given below: | Some Standard Algebraic Identities list are given below: | ||
'''Identity I | === '''Identity I''' === | ||
<math>(a+b)^2=a^2+2ab+b^2</math> | |||
Example: Evaluate <math>(x+3)(x+3)</math> using the identities | Example 1: Evaluate <math>(x+3)(x+3)</math> using the identities | ||
<math>(x+3)(x+3)= x^2+2(x)(3)+3^2</math> | <math>(x+3)(x+3)= x^2+2(x)(3)+3^2</math> | ||
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<math>= x^2+6x+9</math> | <math>= x^2+6x+9</math> | ||
Example 2: Factorise <math>49a^2+70ab+25b^2</math> | |||
<math>49a^2=(7a)^2</math> , <math>25b^2=(5b)^2</math> , <math>70ab=2(7)(5)ab</math> | |||
<math>(7a)^2+2(7)(5)ab+(5b)^2</math> | |||
using the identity 1 <math>a=7a , b = 5b</math> | |||
'''Identity IV | <math>49a^2+70ab+25b^2 = (7a+5b)^2 = (7a+5b)(7a+5b)</math> | ||
=== '''Identity II''' === | |||
<math>(a-b)^2=a^2-2ab+b^2</math> | |||
=== '''Identity III''' === | |||
<math>a^2-b^2=(a+b)(a-b)</math> | |||
=== '''Identity IV''' === | |||
<math>(x+a)(x+b)=x^2+(a+b)x+ab</math> | |||
Example: Evaluate <math>103 \times 105</math> using the identities | Example: Evaluate <math>103 \times 105</math> using the identities | ||
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<math>=10000+800+15=10815</math> | <math>=10000+800+15=10815</math> | ||
=== '''Identity V''' === | |||
<math>(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca</math> | |||
'''Identity | === '''Identity VI''' === | ||
<math>(a+b)^3=a^3+b^3+3ab(a+b)</math> | |||
'''Identity VII | === '''Identity VII''' === | ||
<math>(a-b)^3=a^3-b^3-3ab(a-b)</math> | |||
'''Identity VIII | === '''Identity VIII''' === | ||
<math>a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)</math> |
Revision as of 13:27, 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 1
Identity II
Identity III
Identity IV
Example: Evaluate using the identities
Identity V
Identity VI
Identity VII
Identity VIII