Squaring brackets

Squaring Brackets

Introduction

  • Squaring brackets refers to multiplying an bracketed term by itself.

  • This process is crucial in algebraic computation and showcases the importance of order of operations and the distributive property.

Squaring Brackets Rule

  • The expression inside the bracket is multiplied by itself. It’s not just squaring the individual terms inside the brackets - the bracketed quantity is treated as a whole.

  • The process follows binomial expansion, resulting in the square of the first term, plus twice the product of the two terms, plus the square of the second term.

Step-by-Step Guide for Squaring Brackets

  1. Identify the term inside the bracket.

  2. Write the bracketed term twice as you’re multiplying it by itself.

  3. Use the FOIL method to multiply out the brackets (First, Outer, Inner, Last terms).

  4. Carefully pay attention to the signs of terms in brackets during the multiplication process.

  5. Combine like terms (if any).

Examples

  • For the equation (x + 3)², The operation will be (x + 3)(x + 3). Applying the FOIL method, you get x² + 3x + 3x + 9, which simplifies to x² + 6x + 9.

  • For the equation (y - 4)², The operation will be (y - 4)(y - 4). Using the FOIL method, it turns into y² - 4y - 4y +16, which simplifies to y² - 8y + 16.

Conclusion

  • Squaring brackets is essential as it serves as the basis for the development of higher-level algebraic calculations.

  • Regular practice is crucial to understand this concept fully and to ensure you remember to apply the FOIL method accurately. Careful attention to signs can help avoid common errors!