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A Plus B Plus C Whole Square

Are you looking for A Plus B Plus C Whole Square? You can check the formulas of A Plus B Plus C Whole Square in three ways. We are going to share the (a+b+c)^2 algebra formulas for you as well as how to create (a+b+c)^2 and proof.

(a+b+c)2

we can write: \( (a+b+c)^2 = (a+b+c)(a+b+c) \)

write simple multiplication form \( (a+b+c)^2 = a \times (a+b+c) + b \times (a+b+c) + c \times (a+b+c) \)

Simplify calculation one by one: \( (a+b+c)^2 = (a^2 +ab+ac) + b \times (a+b+c) + c \times (a+b+c) \)

\(=> (a+b+c)^2 = (a^2 +ab+ac) + (ab + b^2 + bc) + c \times (a+b+c) \)

\(=> (a+b+c)^2 = (a^2 +ab+ac) + (ab + b^2 + bc) + (ac+bc + c^2) \)

Arrange \( (a+b+c)^2 = a^2 +ab+ac + ab + b^2 + bc + ac+bc + c^2 \)

\(=> (a+b+c)^2 = a^2 +ab + ab + b^2 + bc + bc + ac + ac+ c^2 \)

Additon same value:\( (a+b+c)^2 = a^2 +2ab + b^2 + 2bc  + 2ac + c^2 \)

Arrage value by Power: \( (a+b+c)^2 = a^2 + b^2 + c^2 + 2bc  + 2ac +2ab \)

(a+b+c)^2 Verifications

Need to verify \( (a+b+c)^2 \) formula is right or wrong. put the value of a = 2, b=3 and c=4

put the value of a and b in the LHS

\(=> (a+b+c)^2 = (2+3+4)^2 \)

\(=> (a+b+c)^2 = (9)^2 \)

\(=> (a+b+c)^2 = 81 \)

put the value of a and b in the RHS

\( => a^2 + b^2 + c^2 + 2bc  + 2ac +2ab \)

\( => 2^2 + 3^2 + 4^2 + 2 \times 3 \times 4  + 2 \times 2 \times 4 +2 \times 2 \times 3 \)

\( => 4 + 9 + 16 + 24  + 16 + 12 \)

\( => 13 + 40  + 28 \)

\( => 53  + 28  = 81\)

Therefore \( LHS = RHS \)

Proof formula \( (a+b+c)^2 = a^2 + b^2 + c^2 + 2bc  + 2ac +2ab \)

Summary (a+b+c)^2

If you have any issues in the (a+b+c)^2 formulas, please let me know through social media and mail. A Plus B Plus C Whole Square is most important algebra maths formulas for class 6 to 12.

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