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*
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