How do you expand closed brackets?

Expanding closed brackets, also known as "multiplying out," is a fundamental algebraic technique used to simplify expressions. It involves distributing the term outside the brackets to each term inside the brackets and then collecting like terms. In essence, you're removing the brackets by performing multiplication.

Understanding the Process

According to the provided reference, expanding brackets involves multiplying every term inside the bracket by the term on the outside and then collecting like terms with the aim of removing the set of brackets. Here's a breakdown of how it works:

Step-by-Step Guide

1. Identify the term outside the bracket: This could be a number, a variable, or a combination of both.

2. Multiply each term inside the bracket by the term outside: Ensure you pay attention to the signs (positive or negative) of each term.

3. Simplify and collect like terms: Combine any terms with the same variable and exponent.

Examples

Let's illustrate the concept with a few examples:

• Example 1: Simple Expansion

  Expand 2(x + 3)

  • Multiply 2 by x: 2 * x = 2x
  • Multiply 2 by 3: 2 * 3 = 6
  • Combine the results: 2x + 6

  Therefore, 2(x + 3) = 2x + 6

• Example 2: Expansion with a Variable

  Expand x(y - 4)

  • Multiply x by y: x * y = xy
  • Multiply x by -4: x * -4 = -4x
  • Combine the results: xy - 4x

  Therefore, x(y - 4) = xy - 4x

• Example 3: Expansion with Multiple Terms

  Expand -3(2a - b + 5)

  • Multiply -3 by 2a: -3 * 2a = -6a
  • Multiply -3 by -b: -3 * -b = 3b
  • Multiply -3 by 5: -3 * 5 = -15
  • Combine the results: -6a + 3b - 15

  Therefore, -3(2a - b + 5) = -6a + 3b - 15

Practical Tips

• Pay attention to signs: A negative sign outside the bracket will change the sign of every term inside.

• Be organized: Write each step clearly to avoid mistakes.

• Double-check your work: After expanding, make sure you've multiplied every term correctly and collected like terms accurately.