Algebra

In Years 7 and 8 you learned to simplify expressions, expand brackets like $3(2x - 5)$ and take out a common factor. In this topic you'll go further: expanding the product of two brackets, such as $(x + 3)(x - 5)$, and reversing the process to factorise expressions like $x^2 + 7x + 12$. These skills unlock the quadratics topic later this year, where factorising is the key to solving equations and sketching graphs.

What you'll learn

• 3.01 Algebra review: terms and coefficients, collecting like terms, multiplying and dividing terms with powers, and substitution.
• 3.02 Distributive law: expanding expressions like $-2x(3x^2 - x + 1)$, then collecting like terms.
• 3.03 Binomial expansion: expanding two brackets like $(2x + 3)(x - 4)$, perfect squares like $(x + 5)^2$, and the difference of two squares.
• 3.04 Algebraic factors: factorising by taking out the highest common factor, including letters, negative factors and whole brackets.
• 3.05 Factorise by grouping: factorising four-term expressions in pairs, and factorising quadratics like $x^2 + 7x + 12$.
• Investigation: calendar expressions. Use algebra to explain the surprising patterns hidden in a calendar.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: simpler expressions and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: longer expressions, harder factorising and proofs, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.