a² + 2ab + b² = (a + b)². a² − 2ab + b² = (a − b)². The middle term is twice the product. Factoring as a set is in factoring quadratics.
Check the middle
x² + 6x + 9 is (x + 3)² because 2×x×3 = 6x. Difference of cubes is a different leftover, in difference of cubes. Polynomials as a set are in polynomials.
The bottom line
First squared, last squared, middle twice the product. Then it is a square.
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