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 ${ ({ F }_{ n+1 }) }^{ 2 }-{ ({ F }_{ n }) }^{ 2 }$ .

55\cdot { 13 }^{ 2 }

89\cdot 21

{ 34 }^{ 2 }

55\cdot 13

{ 34 }^{ 2 }+{ 13 }

{ 34 }^{ 2 }+{ 13 }^{ 2 }

55\cdot 21

{ 21 }^{ 2 }