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Prove the polynomial identity 1. x ^ 2 - y ^ 2 = (x - y)(x + y)

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Explanation:

Expand the right side using the distributive property, then collect terms.

  x² -y² = (x -y)(x +y)

  = (x)(x +y) -y(x +y)

  = x² +xy -yx -y²

  = x² +(xy -xy) -y²

  = x² -y² . . . . . . . . . . as required

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