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

Math Staff asked 6 months ago

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

#### 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
$\ (a+b)^4 = a^4 + a^2 b^2 + b^2 a^2 + 4a^2b^2 + b^4 + 2ab^3 + 2ab^3 + 2a^3 b + 2a^3 b$
$\ (a+b)^4 = a^4 + 6a^2b^2 + b^4 + 4ab^3 + 4a^3 b$
$\ (a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4$