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.

.

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) (x² – xy + y²)
• x³ – y³ = (x – y) (x² + 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)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 = a³+ b³+ c³+ 6abc + 3ab(a+b) + 3ac(a+c) + 3bc(b+c) put the value of a = 1, b=2 and c=3

FAQs on a b c whole cube formula

From here you can download important Books and PDF related to Mathematics – Quantitative aptitude – Click

Download Study material / Class notes / Books for UPSC Exams preparation – Check this website