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To square 75, one can multiply (70)(80) and add 25 to that product. Can someone explain how this would work, without calculating?

  • math -

    since a^2-b^2 = (a-b)(a+b)
    a^2 = (a-b)(a+b)+b^2

    75^2 = (75-5)(75+5)+5^2 = (70)(80)+25

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