## What is the formula of A plus B plus C whole Cube (a + b + c)^{3}

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What are various forms to write (A+B+C) a whole cube? and What is the identity for a+b+c3. A plus B plus C whole Cube formula is an algebraic identity which is used to find the sum of cubes of the three numbers. The expression of this A plus B plus C ka whole cube formula is **(a + b + c)³ = a³ + b³ + c³ + 3 (a +b) (b + c) (a+ c)**. Read about a b c whole cube or What’s the formula for (a+b+c) the whole cube.

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### How to derive A plus B plus C the whole cube ka formula

Lets understand this (a + b + c)^{3 }Formula in details or what is the proof of formula of whole cube of a+b+c. this formula is the sum of the cubes of three numbers.

We can derive this formula A plus B plus C whole cube (a + b + c)^{3} formula by just multiplying (a+b+c)^{2} A plus B plus C whole square by (a+b+c). so here we will see the expansion of A plus B plus C ka whole cube.

**The Formula is : (a + b + c)³ = a³ + b³ + c³ + 3 (a +b) (b + c) (a+ c)**

**What is the value of a+b+c^3**Explanation : Let us just start with (a+b+c)² = a² +b² + c²+2ab+2bc+2ca and rewrite this expression as equation 1.

Equation 1 – (a+b+c)² = a² +b² + c²+2(ab+bc+ca), Now: Multiply equation 1 with (a+b+c) both side.

- (a+b+c)² (a+b+c) =
**(a + b + c)³ =**[a² +b² + c²+2(ab+bc+ca)](a+b+c)**(a + b + c)³****= a**²[a+b+c] +b²[a+b+c]+c²[a+b+c] +2[(ab+bc+ca)[a+b+c]]**(a + b + c)³**= a³+a²b+a²c + b²a+b³+b²c + c²a +c²b +c³ + 2ab[a+b+c] +2bc(a+b+c) +2ca(a+b+c)**(a + b + c)³ =**a³+a²b+a²c + b²a+b³+b²c + c²a +c²b +c³ +2a²b+2ab²+2abc +2abc+2b²c +2bc² +2a²c +2abc +2a²c**(a + b + c)³ =**a³+b³+c³+6abc +a²b+2a²b+a²c + b²a+b²c+2ab² +c²a+c²b+2c²b- (a + b + c)
^{3}= a^{3}+ b^{3}+ c^{3}+3a^{2}b+3a^{2}c + 3b^{2}c +3b^{2}a +3c^{2}a +3c^{2}a+6abc - (
**a + b + c)³ =**a³+b³+c³+6abc+3a²[b+c] +3b²(a+c) +3c²(a+b) **(a + b + c)³ =**a³+b³+c³+6abc+3[a²[b+c] +b²(a+c) +c²(a+b)]- (a + b + c)
^{3}= a^{3}+ b^{3}+ c^{3}+ 6abc + 3ab(a+b) + 3ac(a+c) + 3bc(b+c)

on further simplifying, we get final expression** (a + b + c)³= a³ + b³ + c³ + 3 [(a +b) (b + c) (a+ c)]**

### List of Some important Algebraic formula

- (x + y + z)
^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy +2yz + 2xz - (x + y – z)
^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy – 2yz – 2xz - (x – y + z)
^{2}= x^{2}+ y^{2}+ z^{2}– 2xy – 2yz + 2xz - (x – y – z)
^{2}= x^{2}+ y^{2}+ z^{2}– 2xy + 2yz – 2xz - x
^{3}+ y^{3}+ z^{3}– 3xyz = (x + y + z) (x^{2}+ y^{2}+ z^{2}– xy – yz -xz) - x
^{3}+ y^{3}= (x + y) (x^{2 }– xy + y^{2}) - x
^{3}– y^{3}= (x – y) (x^{2 }+ xy + y^{2}) - (a – b)
^{3}= a^{3}– b^{3}– 3ab (a – b) - (a + b)
^{3}= a^{3}+ b^{3}+ 3ab (a + b) - (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a – b)
^{2}= a^{2}– 2ab + b^{2} - (a + b) (a – b) = a
^{2}– b^{2} - (a + b)
^{4}= a^{4}+ 4a^{3}b + 6a^{2}b^{2}+ 4ab^{3}+ b^{4} - (a – b)
^{4}= a^{4}– 4a^{3}b + 6a^{2}b^{2}– 4ab^{3}+ b^{4}

### Solved examples using by (a + b + c)^{3} formula

Now you can understand the formula of a+b+c whole cube (a+ b + c)^{3 }= **a³ + b³ + c³ + 3 (a +b) (b + c) (a+ c)** or a3 + b3 + c3+3a2b+3a2c + 3b2c +3b2a +3c2a +3c2a+6abc in detail by solving some good examples

**Example 1: **Proof (a + b + c)^{3 }algebraic identity formula is correct or wrong ?. if a = 1, b = 2 and c = 3

**Solution:** First you should know the formula of a plus b plus c whole cube. (a + b + c)^{3} = a^{3}+ b^{3}+ c^{3}+ 6abc + 3ab(a+b) + 3ac(a+c) + 3bc(b+c) put the value of a = 1, b=2 and c=3

LHS is equal to (a + b + c)^{3} = (1+2+3)^{3} = 6^{3} = 216

RHS is equal to a^{3}+ b^{3}+ c^{3}+ 6abc + 3ab(a+b) + 3ac(a+c) + 3bc(b+c)

3+2^{3}+3^{3}+6×1×2×3+3×1×2(1+2)+3×1×3(1+3)+3×2×3(2+3)

1+8+27+36+6(3)+9(4)+18(5)

36+36+18+36+90

72+54+90

126+90=216

**Answer:** Therefore LHR=RHS

#### FAQs on a b c whole cube formula

**What Is the Expansion of (a + b + c)**

^{3}Formula?A plus B plus C ka whole cube formula is (a + b + c)3 = a3+ b3+ c3+ 6abc + 3ab(a+b) + 3ac(a+c) + 3bc(b+c). Read about a b c whole cube **(a + b + c)³= a³ + b³ + c³ + 3 [(a +b) (b + c) (a+ c)]**.

**What Is the**

**(a + b + c)³**Formula in Algebra?**(a + b + c)³= a³ + b³ + c³ + 3 [(a +b) (b + c) (a+ c)]**

**What is the formula for a b c whole cube?**

**(a + b + c)³= a³ + b³ + c³ + 3 [(a +b) (b + c) (a+ c)]** or (a + b + c)^{3} = a^{3}+ b^{3}+ c^{3}+ 6abc + 3ab(a+b) + 3ac(a+c) + 3bc(b+c) or (**a + b + c)³ =** a³+b³+c³+6abc+3a²[b+c] +3b²(a+c) +3c²(a+b).

**How do you solve an ABC whole cube?**

(**a + b + c)³ =** a³+b³+c³+6abc+3a²[b+c] +3b²(a+c) +3c²(a+b)

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