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## A Plus B Plus C Whole cube

Are you looking for A plus B plus C Whole cube? You can check the formulas of A plus B plus C Whole cube in three ways. We are going to share the (a+b+c)^3 algebra formulas for you as well as how to create (a+b+c)^3 and proof.

we can write: $$(a+b+c)^3 = (a+b+c)(a+b+c)(a+b+c)$$

$$=>(a+b+c)^3 = (a+b+c)^2 (a+b+c)$$ [we know that what is the formula of $$(a+b+c)^2$$]

$$=>(a+b+c)^3 = (a^2+b^2+c^2 + 2ab +2bc +2ca) (a+b+c)$$

need too write in simple form of multiplication $$=>(a+b+c)^3 = a \times (a^2+b^2+c^2 + 2ab +2bc +2ca)\\ + b \times (a^2+b^2+c^2 + 2ab +2bc +2ca)\\ + c \times (a^2+b^2+c^2 + 2ab +2bc +2ca)$$

Simplify the all Multiplication one by one $$(a+b+c)^3 = a \times (a^2+b^2+c^2 + 2ab +2bc +2ca)\\ + b \times (a^2+b^2+c^2 + 2ab +2bc +2ca)\\ + c \times (a^2+b^2+c^2 + 2ab +2bc +2ca)$$

$$=> (a+b+c)^3 = (a^3+ab^2+ac^2 + 2a^2b + 2abc + 2ca^2)\\ + b \times (a^2+b^2+c^2 + 2ab +2bc +2ca)\\ + c \times (a^2+b^2+c^2 + 2ab +2bc +2ca)$$

$$=> (a+b+c)^3 = (a^3+ab^2+ac^2 + 2a^2b + 2abc + 2ca^2)\\ + (a^2b+b^3+bc^2 + 2ab^2 + 2b^2c +2abc)\\ + c \times (a^2+b^2+c^2 + 2ab +2bc +2ca)$$

$$=> (a+b+c)^3 = (a^3+ab^2+ac^2 + 2a^2b + 2abc + 2ca^2)\\ + (a^2b+b^3+bc^2 + 2ab^2 + 2b^2c +2abc)\\ + (ca^2 + cb^2 + c^3 + 2abc + 2bc^2 + 2c^2a)$$

Arrage value according power and similear

$$=> (a+b+c)^3 = a^3 + b^3 +c^3 \\+ 6abc + 3a^2b+ 3ab^2 \\ + 3ac^2 + 3bc^2 +3b^2c + 3a^2c$$

$$=> (a+b+c)^3 = \\a^3 + b^3 +c^3 + 6abc+ 3ab (a+b) + 3ac (a+c) + 3bc (b+c)$$

### (a+b+c)^3 Verifications

Need to verify $$(a+b+c)^3$$ formula is right or wrong. put the value of a = 1, b=2 and c=3

put the value of a and b in the LHS

$$(a+b+c)^3 = (1+2+3)^3$$

$$6^3 = 216$$

put the value of a and b in the RHS

$$=> a^3 + b^3 +c^3 + 6abc+ 3ab (a+b) + 3ac (a+c) + 3bc (b+c)$$

$$=> 1^3 +2^3+3^3 +6 \times 1 \times 2 \times 3 + 3 \times 1 \times 2 (1+2) \\ + 3 \times 1 \times 3 (1+3) + 3 \times 2 \times 3 (2+3)$$

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

$$=> 36 +36 + 18 +36 + 90$$

$$=> 72 + 54 + 90$$

$$=> 126 + 90 =216$$

Therefore $$LHR = RHS$$

#### Summary (a+b+c)^3

If you have any issues in the (a+b+c)^3 formulas, please let me know through social media and mail. A Plus B Plus C Whole cube is most important algebra maths formulas for class 6 to 12.