We substitute a = 3x, b = -2y and c = 4z into the expansion formula. Squaring terms makes them positive, while the cross-products involving the negative y term become negative.
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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.
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.