A Plus B Whole Four (a+b)^4
Are you looking for a plus b whole four? You can check the formulas of a plus b whole four in three ways. We are going to share the (a+b)^4 algebra formulas for you as well as how to create (A+B)^4 and proof.
we can write \( (a+b)^4 = (a+b)^2 \times (a+b)^2 \)
[Note: We know a plus b whole square formula: \( (a+b)^2 = a^2 + b^2 +2ab \)]
\( (a+b)^4 = (a^2 + b^2 +2ab) \times (a^2 + b^2 +2ab) \)
Brack braket into multiplciation form
\( (a+b)^4 = (a^2 + b^2 +2ab) \times a^2 \\ + (a^2 + b^2 +2ab) \times b^2 \\ + (a^2 + b^2 +2ab) \times 2ab \)
start multiplication
\( (a+b)^4 = (a^4 + b^2 a^2 +2a^3b) \\ + (a^2 b^2+ b^4 +2ab^3) \\ + (2a^3b + 2ab^3 +4a^2b^2) \)
simplify Calculation with arrage power and same value
\( (a+b)^4 = a^4 + b^4 + 6a^2b^2 + 4a^3b +4b^3a \)
we can also write like this \( (a+b)^4 = a^4 + b^4 + 6a^2b^2 + 4ab (a^2 + b^2) \)
(A+B)^4 Verifications
Need to verify \( (a+b)^4 \) formula is right or wrong. put the value of a =1 and b=2
put the value of a and b in the LHS
\( => (a+b)^4 = (1+2)^4 \)
\( => (a+b)^4 = (3)^4 \)
\( => (a+b)^4 = 81 \)
put the value of a and b in the RHS
\( a^4 + b^4 + 6a^2b^2 + 4ab (a^2 + b^2) \)
\( 1^4 + 2^4 + 6 \times 1^2 \times 2^2 + 4\times 1\times 2 (1^2 + 2^2) \)
Simplify calculation: \( 1 + 16 + 6 \times 1 \times 4 + 4\times 1\times 2 (1 + 4) \)
\( 1 + 16 + 24 + 8 (5) \)
\( 1 + 40 + 40 = 81 \)
Therefore \( LHS =RHS \) [Note: LHS =Left hand Side, RHS =Right hand side]
Proof Formula: \( (a+b)^4 = a^4 + b^4 + 6a^2b^2 + 4ab (a^2 + b^2) \)
Summary (A+B)^4
If you have any issues in the (A+B)^4 formulas, please let me know through social media and mail. A Plus B Whole Four is the most important algebra maths formulas for class 6 to 12.