# What is Formula of a plus b whole four $$(a+b)^4$$?

## What is a plus b whole four $$(a+b)^4$$ Formula

There are multiples ways to find out the result of $$(a+b)^4$$ formula.

=> we can write  $$(a+b)^4 = {(a+b)^2}^2$$ [we know that $$(a+b)^2 = a^2+b^2+2ab$$ ]

$$= (a^2+b^2+2ab)^2$$ [we know that $$(a+b+c)^2 = a^2+b^2+c^2 + 2ab +2bc +2ca$$ ]

we need to put the value of $$a = a^2, b= b^2 \; and \; c=2ab$$

$$= (a^2)^2 + (b^2)^2 + (2ab)^2 + 2a^2 b^2 + 2 b^2 \times 2ab + 2 a^2 \times 2ab$$

$$= a^4 + b^4 + 4a^2b^2 + 2a^2 b^2 + 4b^3a + 4a^3b$$

$$= a^4 + b^4 + 6a^2b^2 + 4b^3a + 4a^3b$$ [Proof]

Now we are going to proof $$(a+b)^4$$ formula by another method.

we can write $$(a+b)^4 = (a+b)^2 (a+b)^2$$ [we know that $$(a+b)^2 = a^2+b^2+2ab$$ ]

$$(a+b)^4 = (a^2+b^2+2ab) (a^2+b^2+2ab)$$

$$= a^2 (a^2+b^2+2ab) + b^2 (a^2+b^2+2ab) + 2ab (a^2+b^2+2ab)$$

$$= a^4+ a^2b^2+2a^3b + b^2 a^2+b^4+2ab^3 + 2a^3b +2ab^3+4a^2b^2$$ [Arrage Simler Value according to power]

$$= a^4 +b^4 + a^2b^2+4a^2b^2 + b^2 a^2+2ab^3 + 2ab^3+ 2a^3b +2a^3b$$ [add Simler Value]

$$= a^4 +b^4 + 6a^2b^2+4ab^3 + 4a^3b$$