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.
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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.
We apply the identity with a = x and b = 1/2y. The middle term simplifies because the number two in the formula cancels out with the denominator two of the fraction.
We substitute a = 3/4 s and b = 8t into the square identity. Squaring the terms independently and simplifying the middle multiplication step gives the final plain algebraic text solution.