This worksheet builds algebraic fluency, teaching students to expand binomial products — including perfect squares and difference of squares — and factorise monic quadratic expressions. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Expanding a binomial product: (x+a)(x+b) = x² + (a+b)x + ab — multiply every term in the first bracket by every term in the second.
- Special products: (x+a)² = x²+2ax+a² (perfect square); (x+a)(x−a) = x²−a² (difference of squares).
- Factorising a monic quadratic (x²+bx+c, leading coefficient 1) means finding two numbers p, q with p+q=b and pq=c, giving (x+p)(x+q).
- If a quadratic has a common factor first, factor that out before factorising the remaining monic quadratic.
- Expanding and factorising are inverse processes — you can always check a factorisation by expanding it back out.
What your child will practise:
- Expanding a binomial product using the distributive law.
- Recognising and expand perfect squares and difference-of-squares products.
- Simplifying an algebraic expression by expanding and collecting like terms.
- Factorising a monic quadratic expression by finding an appropriate pair of numbers.
- Factoring out a common numerical factor before factorising the remaining quadratic.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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