The expression follows the pattern of a square + 2ab + b square. Since 9x square is (3x) square and 16y square is (4y) square, we can compress it directly into (3x + 4y) square.
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We express 205 as 200 + 5 and use our identity where a = 200 and b = 5. Calculating the individual parts and adding them up gives the final numerical answer.
We transform 105 into 100 + 5 and apply the identity with a = 100 and b = 5. Adding the squared values to the middle cross-product gives the correct total.
We rewrite 64 as 60 + 4 to use the identity with a = 60 and b = 4. Summing the squares of 60 and 4 with their double product yields 4096.
We substitute a = 1/x and b = 1/y into the identity. Finding the squares of these fractional variables and combining their cross-product gives the final simplified rational terms.