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Math

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Show that (a^2+b^2)(c^2+d^2)=(ac+bd)^2 + (ad-bc)^2

  • Math - ,

    Foil Left side gives you:
    = a^2c^2 + a^2d^2 + b^2c^2 + b^2d^2
    = (ac)^2 + (ad)^2 + (bc)^2 + (bd)^2

    Foil Right side (ac+bd)^2
    = ac x ac + ac x bd + ac x bd + bd x bc
    = (ac)^2 + 1acbd + 1acbd + (bd)^2

    Foil (ad-bc)^2
    = ad x ad - bc x ad - bc x ad + bc x bc
    = (ad)^2 - 1acbd - 1acbd + (bc)^2

    Combine all terms on right side
    left with (ac)^2 + (bd)^2 + (ad)^2 + (bc)^2

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