Is this even possible?

Algebra Level 5

Given that \(a+b=3\) and \(a^{2}+b^{2}=7\), find the value of

\[a^{10}+2a^{9}b+3a^{8}b^{2}+4a^{7}b^{3}+5a^{6}b^{4}\] \[+6a^{5}b^{5}+5a^{4}b^{6}+4a^{3}b^{7}+3a^{2}b^{8}+2ab^{9}+b^{10}.\]

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