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Math Help - Help, Multiplying binomial radicals

  1. #1
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    Question Help, Multiplying binomial radicals

    I've looked through dozens and dozens of questions, and I can't find an example with this format where both numbers in both sides are under the radical sign, and no numbers to the left, please help. (sqrt 3+4)(sqrt 3-7) The answer is 25-3-sqrt3 how do I get there??
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  2. #2
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    Re: Help, Multiplying binomial radicals

    What happens when you multiply through using the pattern (a+b)(c+d)=ac+ad+bc+bd?
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  3. #3
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    Re: Help, Multiplying binomial radicals

    Hello, drmattthew!

    \left(\sqrt{3} + 4\right)\left(\sqrt{3}-7\right)

    Multiply as usual ("FOIL") . . . and simplify carefully.

    \left(\sqrt{3}+4\right)\left(\sqrt{3}-7\right) \;=\;\big(\sqrt{3}\big)\big(\sqrt{3}\big) + \big(\sqrt{3}\big)\big(\text{-}7\big) + \big(4\big)\big(\sqrt{3}\big) + \big(4\big)\big(\text{-}7\big)

    n . . . . . . . . . . . . . =\qquad\quad 3 \quad\;\;-\;\quad 7\sqrt{3} \quad+\quad 4\sqrt{3} \quad-\quad 28

    n . . . . . . . . . . . . . =\qquad\qquad \text{-}25 \;\;-\;\; 3\sqrt{3}
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