What is the formula for (a+b)^4?

Math Staff asked 6 months ago

Answer:

\[\ (a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 \]

Explanation:

\[\ (a+b)^4 = (a+b)^2 \times (a+b)^2 \]

\[\ (a+b)^2 = a^2 + b^2 + 2ab \]

\[\ (a+b)^4 = (a^2 + b^2 + 2ab) \times (a^2 + b^2 + 2ab) \]

Multiplication

\[\  (a^2 ) \times (a^2 + b^2 + 2ab) = a^4 + a^2  b^2 + 2a^3 b  \]

\[\  (b^2 ) \times (a^2 + b^2 + 2ab) = b^2 a^2 + b^4 + 2ab^3 \]

\[\  ( 2ab) \times (a^2 + b^2 + 2ab) =  2a^3 b + 2ab^3 + 4a^2b^2 \]
Put The Value in a Single Row
\[\ (a+b)^4 = a^4 + a^2  b^2 + 2a^3 b + b^2 a^2 + b^4 + 2ab^3 + 2a^3 b + 2ab^3 + 4a^2b^2 \]
Arrange in Sequence
\[\ (a+b)^4 = a^4 + a^2  b^2 + b^2 a^2 + 4a^2b^2 + b^4 + 2ab^3 + 2ab^3 + 2a^3 b + 2a^3 b \]
Add Similar Value
\[\ (a+b)^4 = a^4 + 6a^2b^2 + b^4 + 4ab^3 + 4a^3 b \]
\[\ (a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 \]