If a+b+c=0. Then find the value of a3 + b3+ c3.

By Ritesh|Updated : November 13th, 2022

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

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.

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