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A plus B plus C whole Cube Formula

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

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) = [a² +b² + c²+2(ab+bc+ca)](a+b+c)
  • (a + b + c)³ = [a² +b² + c²+2(ab+bc+ca)](a+b+c)
  • (a + b + c)³ = a²[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 = a3 + b3 + c3+3a2b+3a2c + 3b2c +3b2a +3c2a +3c2a+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 = a3+ b3+ c3+ 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 = x2 + y2 + z2 + 2xy +2yz + 2xz
  • (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
  • (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
  • (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
  • x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz -xz)
  • x3 + y3 = (x + y) (x– xy + y2)
  • x3 – y3 = (x – y) (x+ xy + y2)
  • (a – b)3 = a3 – b3 – 3ab (a – b)
  • (a + b)3 = a3 + b3 + 3ab (a + b)
  • (a + b)2 = a2 + 2ab + b2
  • (a – b)2 = a2 – 2ab + b2
  • (a + b) (a – b) = a2 – b2
  • (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
  • (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4

Solved examples using by (a + b + c)3 formula

Now you can understand the formula of a+b+c whole cube (a+ b + c)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)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 = a3+ b3+ c3+ 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 = 63 = 216

RHS is equal to a3+ b3+ c3+ 6abc + 3ab(a+b) + 3ac(a+c) + 3bc(b+c)

3+23+33+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 = a3+ b3+ c3+ 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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