FOIL Method for Multiplying Binomials

Key Terms

• FOIL: Acronym for First, Outer, Inner, Last. It's a method used to multiply two binomials.
• Radicand: The number inside a radical symbol.

Steps to Multiply Binomials Using FOIL

1. First Terms: Multiply first terms in each binomial.
   • Example: (7 \times 2 = 14)
2. Outer Terms: Multiply outer terms in each binomial.
   • Example: (7 \times -3 \sqrt{5} = -21 \sqrt{5})
3. Inner Terms: Multiply inner terms in each binomial.
   • Example: (4 \times 2\sqrt{5} = 8 \sqrt{5})
4. Last Terms: Multiply last terms in each binomial.
   • Example: (4\sqrt{5} \times -3 \sqrt{5} = -12 \sqrt{25})

Combining Like Terms

• Middle terms with like radicands (same number inside the radical) can be combined.
  • Example: (-21 \sqrt{5} + 8 \sqrt{5} = -13 \sqrt{5})

Simplifying

• Simplify radicals where possible.
  • Example: (\sqrt{25} = 5)
  • Result: (-12 \times 5 = -60)
• Combine constant terms.
  • Example: (14 - 60 = -46)

Final Result

• Combine all parts to get the final result.
  • Example: ( -46 - 13 \sqrt{5} )