Squaring binomials with radicals

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carlywelch carlywelch
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Squaring binomials with radicals

How would you square (√d+3) + (√d+7)
AlgebraHouse AlgebraHouse
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Re: Squaring binomials with radicals

Just the FOIL method / distributive property.  The FOIL method and distributive property are the same when multiplying two binomials.  However, this is a bit complex, so brace yourself for the following:

[(√d + 3) + (√d + 7)]²
= [(√d + 3) + (√d + 7)][(√d + 3) + (√d + 7)]   {when squaring a binomial, multiply it by itself}
= [(√d + 3)(√d + 3) + (√d + 3)(√d + 7) + (√d + 7)(√d + 3) + (√d + 7)(√d + 7)]   {FOIL method}
= [(d + 6√d + 9) + (d + 7√d + 3√d + 21) + (d + 3√d + 7√d + 21) + (d + 14√d + 49)  {FOIL again}
= [d + 6√d + 9 + d + 10√d + 21 + d + 10√d + 21 + d + 14√d + 49}   {removed parentheses and combined like terms}
= 4d + 40√d + 100   {combined like terms}

- Algebra House