Fibonacci squares

Algebra Level 2

\[\large 1,1,2,3,5,8,13,21,34,55,89, \cdots \]

The above is the Fibonacci sequence, where \(F_n\) is the \(n\)th Fibonacci number with \(F_1 = F_2 = 1\).

Without using a calculator, find which answer is equivalent to \({ ({ F }_{ 10 }) }^{ 2 }-{ ({ F }_{ 9 }) }^{ 2 }\).

\( \)

Hint: Try to find a simpler formula for \({ ({ F }_{ n+1 }) }^{ 2 }-{ ({ F }_{ n }) }^{ 2 }\).

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