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.
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.