Year 9 Maths • AC9M9A02 • Authored homework
Algebraic expressions, expansion and factorising
Expand, simplify and factorise algebraic expressions, including products of binomials and expressions with common factors, while checking answers by reversing the process. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
Expand 4(x + 3).
Factorise 6x + 18.
Expand (x + 2)(x + 5).
Simplify 3a + 4b - a + 2b.
Factorise x^2 + 7x + 10.
Expand 2(3x - 4) - 5.
Identify the highest common factor in 12x^2 + 18x.
Factorise 9y^2 - 16 as a difference of squares.
Correct this error: 3(x + 4) = 3x + 4.
Explain how expansion and factorising are inverse processes.
Part B
Long-answer questions
Expand and simplify 3(2x - 5) + 4(x + 7).
Factorise 15x^2y - 10xy^2 fully and explain how you chose the common factor.
Expand (2x - 3)(x + 5), then substitute x = 2 to check the result.
Factorise x^2 - 9 and explain why it is a difference of squares.
A rectangle has side lengths x + 4 and x + 7. Write and expand an expression for its area.
A student factorises 8x + 12 as 2(4x + 12). Explain why this is incomplete and correct it.
Compare using an area model and distributive law to expand a pair of binomials.
Create a quadratic expression that factorises into two binomials, then expand to verify.
Solve a practical area problem that requires expanding and then simplifying an algebraic expression.
Write a full worked response showing expansion, simplification, factorisation and checking by substitution.
Part C
Research and understanding task
Find a real or designed rectangular area problem where side lengths are algebraic expressions. Model the area, expand it, factorise it if possible, and explain what each expression represents.