This expression matches the identity template a square – 2ab + b square. The middle variable terms cancel out completely when multiplying p/4 and 4/p, leaving only the constant integer minus 2.
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The polynomial matches the identity template a square – 2ab + b square. Since 16y square is (4y) square and 9 is (3) square, it condenses directly into (4y – 3) square.
We rewrite 214 as 200 + 10 + 4 and apply the identity for the square of a three-term sum. Summing the three individual squares and their cross-products gives 45796.
We rewrite 78 as 80 – 2 to use the subtraction identity with a = 80 and b = 2. Combining their squared values and subtracting the double product gives the final result.
We match this with the identity a square + 2ab + b square. Here, 64p square is (8p) square and 4/9 q square is (2/3 q) square, which simplifies cleanly to the factor (8p + 2/3 q) square.