a + b + c Whole Cube: Identity, Formula with Solved Examples
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We use many algebraic identities to solve mathematical problems in our daily lives. a + b + c whole cube is an algebraic identity that is used to find the value of a cube of sum of three numbers.
The expression for the value of a + b + c whole cube is given as:
(a+b+c)3=a3+b3+c3+3(a+b)(b+c)(c+a)
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In this article, we shall learn about this algebraic identity in detail along with its derivation and some solved examples for better understanding of the concept.
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What Is the (a + b +c) whole cube Formula?
a + b + c whole cube is used to find the cube of the sum of three real numbers. The formula can be used to factorize some special type of functions. The formula is written as:
(a+b+c)3=a3+b3+c3+3(a+b)(b+c)(c+a)
Let us derive formula using simple mathematical operations:
Proof:
It can be written as:
Consider the L.H.S of equation (1),
=
=
=
=
=
=
=
=
=
= 3 (a + b) ( b + c) ( a + c )
which is equal to R.H.S of equation (1).
Hence Proved.
Summary
Let us summarize what we have learnt about a + b + c whole cube:
- a + b + c whole cube formula is used to find the cube of the sum of three real numbers.
- The formula or the algebraic identity to find the value of a + b + c whole cube is written as:
. - Here, a, b and c are real numbers.
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a + b + c Whole Cube Solved Examples
Example 1: Prove the correctness of the formula a + b + c whole cube by taking a= 1, b = 2, and c = 3.
Solution: We know that the value of a + b + c whole cube is written as:
Given that:
a = 1, b = 2 and c = 3. Let us substitute the values of a, b, and c in the above formula:
We need to prove LHS = RHS,
LHS =
LHS =
= (6)^3 = 216
RHS =
=
=
=
= 216
Hence Proved.
Example 2: Find the value of
Solution: We know that:
Let us write 12 as 3 + 4 + 5.
Using the identity:
Therefore,
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FAQ’s for a + b + c Whole Cube
How do you solve an A+B+C cube whole?
A + B+ C whole cube can be solved using the formula:
What is the identity of a+ b whole cube?
The identity to solve a +b whole cube gives:
What is the rule of a3+ b3 +c3?
Using the mathematical identity:
What is A plus B minus C whole cube?
Using the mathematical identity:
What Is the (a - b)^3 Formula in Algebra?
The mathematical identity for
What makes the (a + b + c)³ formula different from (a + b)³?
The (a + b + c)³ formula includes three variables and a more complex expansion. It accounts for not just individual cubes but also the interaction between all three terms, unlike (a + b)³ which only has two terms and a simpler identity.
Is it necessary to use this identity in every cube-related problem?
No, it's not always necessary. This identity is especially useful when dealing with three variables added together. If the expression is already in a single number, direct cubing is often quicker.