We rewrite 79 as 80 – 1 to use the subtraction square identity with a = 80 and b = 1. Combining their squared values and subtracting the double product gives 6241.
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Following the hint in the book, we factor out 1/3 as a common factor. This leaves the expression 9a square + 12ab + 4b square inside brackets, which factors into (3a + 2b) square.
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.
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 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.