GCSE Maths Practice: order-of-operations-bidmas

Question 3 of 10

This higher-tier question combines two powers, division, and subtraction to test your full understanding of BIDMAS sequencing.

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\( \begin{array}{l}\text{Evaluate } (5+4)^2 - (3-1)^3 \div 2 \text{ using BIDMAS.}\end{array} \)

Choose one option:

Handle each bracket and power separately before dividing and subtracting. Never subtract before completing the powers.

Working with Multiple Powers in One Expression

Higher-tier BIDMAS questions often combine two or more powers and expect you to apply them in the correct sequence. When powers are linked by subtraction or division, careful step-by-step logic is essential. The golden rule remains the same: finish brackets first, then indices (powers), followed by division or multiplication, and finally addition or subtraction.

Breaking Down Complex Expressions

When you meet an expression that contains two bracketed sections, treat each bracket as a separate mini-calculation. Simplify the values inside them before applying powers. Once both powers are evaluated, check whether they are connected by multiplication, division, or subtraction. Each link changes the order in which you combine the results.

Step-by-Step Strategy

  1. Brackets: Simplify all brackets individually before doing anything else.
  2. Powers: Apply the squares, cubes, or higher indices immediately after the brackets. Powers take priority over every other operation except brackets.
  3. Division and Multiplication: Handle these next, moving from left to right if more than one appears.
  4. Addition and Subtraction: Complete these last to produce the final total.

Writing one operation per line helps keep the logic clear. Each stage should leave you with a simpler expression than before.

Common Mistakes

  • Subtracting before completing both powers.
  • Squaring only the last number rather than the entire bracket.
  • Dividing the wrong part of the expression because brackets were ignored.
  • Rushing through steps without checking sign changes between operations.

To avoid these, underline each power and bracket before starting. Check them off when complete.

Understanding the Role of Powers

Powers act as accelerators: they magnify or reduce numbers dramatically. Squaring a number multiplies it by itself once, while cubing multiplies it by itself twice. Because these operations change values so strongly, they must be performed before other steps to keep every calculation consistent and logical.

Real-World Relevance

Two-power problems mirror real-life models such as comparing areas and volumes. For example, one term might represent a square (length²) and another a cube (volume). Subtracting or dividing them could describe efficiency differences or scaling factors. Following BIDMAS ensures your reasoning stays scientifically valid.

Checking Your Work

After reaching a result, review the order: brackets → powers → division → subtraction. If you see that subtraction was done earlier, revisit the work. Always verify that both powers were applied before any other operation.

FAQs

Q1: What happens if both powers have the same index?
A: Evaluate each separately and then apply the operation between them. The order rule doesn’t change.

Q2: Does it matter which power appears first?

A: Yes, only if subtraction or division is involved; follow the expression from left to right after completing powers.

Q3: How can I avoid missing steps?

A: Use a structured layout with one completed operation per line. Label each line (B for brackets, P for powers, D/M for division or multiplication, A/S for addition or subtraction).

Study Tip

Practise writing full working, even when using a calculator. Show each stage clearly so you can confirm that all powers were finished before subtraction or division. This habit earns full method marks and builds precision needed for higher-tier algebra and problem-solving questions.