Difference of squares

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Recognizing a difference of squares is a commonly used factoring technique in algebra. It refers to the identity $a^2 - b^2 = (a+b)(a-b)$. Note that this identity depends only on the (right and left) distributive property and the commutative property of multiplication and so holds not only for real or complex numbers but also for polynomials, in arithmetic modulo $m$ for any positive integer $m$, or more generally in any commutative ring. However, due to matrices not being commutative under multiplication, this identity doesn't hold for matrices.

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