A Plus B Whole Cube
Are you looking for a plus b whole Cube? You can check the formulas of a plus b whole Cube in three ways. We are going to share the (a+b)^3 algebra formulas for you as well as how to create (A+B)^3 and proof.
we can write \( (a+b)^3 = (a+b)^2 \times (a+b) \)
we know that what is the formulas of a plus b whole square. \(a+b)^2 = a^2 +b^2+2ab \) put the formulas.
\(=> (a+b)^3 = (a^2+b^2+2ab) \times (a+b)\)
\(=> (a+b)^3 = a \times (a^2+b^2+2ab) + b \times (a^2+b^2+2ab)\)
start multiplication
\(=> (a+b)^3 = a^3 + ab^2 + 2a^2 b + ba^2 + b^3 + 2ab^2 \)
Arrange
\(=> (a+b)^3 = a^3 + ab^2 + 2ab^2+ 2a^2 b + ba^2 + b^3 \)
\(=> (a+b)^3 = a^3 + 3 ab^2 + 3a^2 b + b^3 \)
(A+B)^3 Verifications
Need to verify \((a+b)^3\) formula si right or wrong. put the value of a =2 and b=3
put the value of a and b in the LHS
\(=> (a+b)^3 = (2+3)^3 \)
\(=> (a+b)^3 = (5)^3 \)
\(=> (a+b)^3 = 125 \)
put the value of a and b in the RHS
\(=> a^3 + 3 ab^2 + 3a^2 b + b^3 \)
\(=> 2^3 + 3\times 2\times 3^2 + 3\times 2^2\times 3 + 3^3 \)
\(=> 8 + 6 \times 9 + 9 \times 4 + 27 \)
\(=> 8 + 54+ 36 + 27 \)
\(=> 8 + 90 + 27 \)
\(=> 125 \)
Therefore \( LHS = RHS \)
Proof Formulas \((a+b)^3 = a^3 + 3 ab^2 + 3a^2 b + b^3 \)
Summary (A+B)^3
If you have any issues in the (A+B)^3 formulas, please let me know through social media and mail. A Plus B Whole Cube is most important algebra maths formulas for class 6 to 13.
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