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If a+b+c=0. Then find the value of a3 + b3+ c3.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Using the below-mentioned identity – a3+b3 + c3= (a+ b + c) (a2 + b2 + c2 – ab – be – ca) + 3abc.
i.e.
a3+b3 + c3 – 3 abc = (a + b + c)(a2 + b2 + c2 –ab–bc-ca)
we know that a + b + c = 0
Substituting the above value we get:
a3+b3 + c3 – 3abc = 0
So
a³+b³+c³=3abc
Table of content
Algebraic Identities
An equation is referred to as an identifier if it holds true regardless of the values of the variables it contains. A mathematical identifier is an equation whose right-hand side value is equal to its left-hand side value for all possible values of the variables. In various branches of mathematics, we can employ a number of standard identifiers. The Binomial statement yields all standard Identities.
An algebraic identifier is a mathematical expression that refers to every value of a variable within it. Polynomials can also be factored in using it. In order to calculate algebraic expressions and solve various polynomials, algebraic identifiers are employed.
Using Substitution Method
- In general, substitution refers to replacing variables or characters with numbers or values.
- The replacement method involves substituting the values for the variables to carry out an arithmetic operation.
Summary:
If a+b+c=0. Then find the value of a3 + b3+ c3.
If a + b + c = 0 then the value of a³+b³+c³=3abc. Algebraic identities are algebraic equations that are always true for every value of variables in them.
