We express 117 as 100 + 10 + 7 and apply the three-term identity. Squaring each number and adding all the double-product combinations yields the correct numerical total.
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We transform 193 into 200 – 7 and apply the subtraction identity with a = 200 and b = 7. Evaluating these components together gives the correct final numerical answer of 37249.
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.
We take out the common factor 1/5 from the entire expression. The remaining polynomial inside is 9s square + 30sv + 25v square, which condenses smoothly into (3s + 5v) square.
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.