EDEXCEL GCSE FOUNDATION MATHS - What are Expanding Brackets

Expanding Brackets in GCSE Foundation Maths

Expanding brackets is a fundamental skill in algebra. It involves multiplying the terms inside the brackets by the term outside.

Key Concepts

• Brackets: These indicate a group of terms that are to be treated as a single unit.
• Multiplication: The process of expanding brackets involves multiplying the term outside the bracket by each term inside.
• Distributive Law: This law states that multiplying a sum by a number is the same as multiplying each term of the sum by that number.

Steps for Expanding Brackets

1. Identify the term outside the bracket.
2. Multiply this term by each term inside the bracket.
3. Simplify the resulting expression by combining like terms.

Examples

Example 1:

Expand the expression: 3(x + 2)

• Step 1: The term outside the bracket is 3.
• Step 2: Multiply 3 by each term inside the bracket: 3 * x + 3 * 2
• Step 3: Simplify the expression: 3x + 6

Example 2:

Expand the expression: -2(4x - 5)

• Step 1: The term outside the bracket is -2.
• Step 2: Multiply -2 by each term inside the bracket: -2 * 4x - (-2) * 5
• Step 3: Simplify the expression: -8x + 10

Example 3:

Expand the expression: (x + 3)(x - 2)

• Step 1: This involves multiplying two brackets together.
• Step 2: Multiply each term in the first bracket by each term in the second bracket:
  • x * x + x * -2 + 3 * x + 3 * -2
• Step 3: Simplify the expression: x² - 2x + 3x - 6 = x² + x - 6

Practice

Try expanding the following expressions:

• 5(2x + 1)
• -3(y - 4)
• (x + 2)(x + 1)

Tips

• Remember the signs: Pay attention to the signs of the terms outside and inside the brackets.
• Use the distributive law: This law can help you understand why expanding brackets works.
• Practice regularly: The more you practice, the better you'll become at expanding brackets.

Conclusion

Expanding brackets is a crucial skill in algebra. By understanding the steps involved and practicing regularly, you can master this skill and gain confidence in solving algebraic problems.