Multiplying Binomials using the FOIL Method

Introduction

• Topic: Using the FOIL method to multiply binomials and convert them into quadratic polynomials.
• FOIL stands for:
  • First
  • Outer
  • Inner
  • Last

Examples

Example 1: Multiplying ( (x + 2)(2x + 3) )

1. First: Multiply the first terms
   • ( x \times 2x = 2x^2 )
2. Outer: Multiply the outer terms
   • ( x \times 3 = 3x )
3. Inner: Multiply the inner terms
   • ( 2 \times 2x = 4x )
4. Last: Multiply the last terms
   • ( 2 \times 3 = 6 )
5. Combine like terms:
   • Result: ( 2x^2 + 7x + 6 )

Example 2: Solving ( (3x + 4)^2 )

1. Rewrite as two binomials: ( (3x + 4)(3x + 4) )
2. Apply the FOIL method:
   • First: ( 3x \times 3x = 9x^2 )
   • Outer: ( 3x \times 4 = 12x )
   • Inner: ( 4 \times 3x = 12x )
   • Last: ( 4 \times 4 = 16 )
3. Combine like terms:
   • Result: ( 9x^2 + 24x + 16 )

Example 3: Involving Negative Numbers ( (x + 1)(2x - 3) )

1. Apply the FOIL method:
   • First: ( x \times 2x = 2x^2 )
   • Outer: ( x \times -3 = -3x )
   • Inner: ( 1 \times 2x = 2x )
   • Last: ( 1 \times -3 = -3 )
2. Combine like terms:
   • Result: ( 2x^2 - x - 3 )

Conclusion

• The FOIL method is useful for converting binomials into standard quadratic form.
• Important to combine like terms after applying the FOIL steps.
• Special cases include squaring a binomial and involving negative numbers.

Additional Resources

• Suggested to view test preparation playlists for further practice.
• YouTube recommendations for related educational videos.