Multiplying (2 + √3)(4 - √3)

Algebra 1 · Axiom Academy

EXAMPLE Multiplying Radical Binomials Use FOIL to multiply , then combine like terms. Expand and simplify . Multiply the two binomials with FOIL, watch how some products stay rational while others keep the , then combine like terms. Nice work — you expanded a radical binomial product with FOIL and combined like terms. Remember: FOIL stands for First, Outer, Inner, Last: multiply the term pairs in that order to hit all four products. Rational rational stays rational: has no radical. Rational irrational stays irrational: a single makes the product irrational. : a radical times itself cancels the radical, here . Combine like terms: add coefficients on matching radicals, , and constants separately, 8 - 3 = 5 . The same FOIL-then-combine routine multiplies any pair of radical binomials — and watching for radicals that cancel is a powerful shortcut throughout algebra.

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