Expanding two or more brackets

Expanding Two or More Brackets

Introduction

  • The process of expanding two or more brackets is a fundamental concept in algebra.
  • This procedure is also known as FOIL (First Outer Inner Last), which represents the order in which the terms should be multiplied.

The Expand Rule

  • In order to expand two brackets, each term in the first bracket is multiplied by each term in the second bracket.
  • The acronym FOIL reminds you to multiply the First terms in each bracket, the Outer terms, the Inner terms, and finally the Last terms in each bracket.
  • Ensure the correct handling of positive and negative numbers.

Step-by-Step Guide for Expanding Two or More Brackets

  1. Identify the terms in the first and second brackets.

  2. Begin by multiplying the first term in the first bracket with the first term in the second bracket.

  3. Then multiply the outer terms (first term in the first bracket and the last term in the second bracket).

  4. Next up, multiply the inner terms (last term in the first bracket and first term in the second bracket).

  5. Finally, multiply the last terms in the first and second bracket.

  6. Combine your results, ensuring that you have managed each term’s sign correctly.

Examples

  • In the expression (x - 2)(x + 3), you multiply ‘x’ and ‘x’ to get x^2, then ‘x’ and ‘3’ to get 3x, then ‘-2’ and ‘x’ to get -2x, finally ‘-2’ and ‘3’ to get -6. This results in the expansion x^2 + x - 6.

  • With the equation (a + 4)(a - 4), ‘a’ and ‘a’ multiply to give a^2, ‘a’ and ‘-4’ multiply to give -4a, ‘4’ and ‘a’ multiply to give 4a, and ‘4’ and ‘-4’ multiply to give -16. This results in the expansion a^2 - 16, bearing in mind that the 4a and -4a cancel out.

Conclusion

  • The ability to expand two or more brackets is a critical foundation for tackling complex algebraic equations.
  • Practice with an assortment of equations and pay close attention to managing positive and negative terms.