<image>The following table is a part of Pascal's Triangle, which helps readers determine the coefficients of the expanded form of expressions like:
$$(a+b)^{n} \text{(with } n \text{ as a positive integer)}$$
Please carefully observe the patterns in the table and fill in the missing coefficients in the expanded form of $$(a+b)^{4}$$.
$$(a+b)=a+b$$ 
$$(a+b)^{2}=a^{2}+2ab+b^{2}$$ 
$$(a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}$$ 
$$(a+b)^{4}=a^{4}+$$ ______ $$a^{3}b+$$ ______ $$a^{2}b^{2}+$$ ______ $$ab^{3}+b^{4}$$. 
