EDEXCEL GCSE HIGHER MATHS - What are Expanding and Factorising Brackets

Expanding and Factorising Brackets

Expanding Brackets

Expanding brackets means multiplying out the terms inside the brackets by the term outside the brackets.

Example:

Expand the expression: 3(x + 2)

• Step 1: Multiply the term outside the bracket (3) by each term inside the bracket.
• 3 * x = 3x

• 3 * 2 = 6

• Step 2: Combine the terms.

• 3x + 6

Therefore, 3(x + 2) expands to 3x + 6.

Important Note: Remember the order of operations (PEMDAS/BODMAS). If there are any other operations within the bracket, perform them first before expanding.

Factorising Brackets

Factorising brackets is the opposite of expanding. It involves finding the common factors of the terms and expressing the expression as a product of a factor and a bracket.

Example:

Factorise the expression: 4x + 8

• Step 1: Find the highest common factor (HCF) of the terms 4x and 8. The HCF is 4.

• Step 2: Divide each term by the HCF:

• 4x / 4 = x

• 8 / 4 = 2

• Step 3: Write the HCF outside the bracket and the results of the division inside the bracket.

• 4(x + 2)

Therefore, 4x + 8 factorises to 4(x + 2).

Tips for Factorising:

• Look for the HCF of the terms.
• Divide each term by the HCF.
• Write the HCF outside the bracket and the results inside the bracket.

Expanding and Factorising Examples:

Expanding:

1. 2(3x - 1) = 6x - 2
2. (x + 2)(x - 3) = x² - x - 6 (Remember to multiply each term in the first bracket by each term in the second bracket)

Factorising:

1. 5x + 10 = 5(x + 2)
2. x² - 9 = (x + 3)(x - 3) (Difference of squares pattern)

Practice:

Work through several examples of expanding and factorising brackets. It is essential to understand these concepts for further algebraic manipulation and problem-solving in GCSE Higher Maths.