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 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 apply the identity by substituting a = 7x and b = 4y. Squaring both individual terms and calculating twice their product gives us the terms 49x square, 56xy, and 16y square.