Mathematics 0580 · IGCSE · Algebraic manipulation

Algebraic manipulation — practice question

Expanding expressions, factorising, indices, and a proof involving odd numbers.
(a)[3]

Expand and simplify the expression $3x(x-2) - 2x(3x-5)$.

(b)[4]

Factorise completely. (i) $6w + 3wy - 4x - 2xy$ (ii) $4x^2 - 25y^2$

(c)[2]

Simplify completely $\left(\frac{16}{9x^4}\right)^{-\frac{3}{2}}$.

(d)[3]

$n$ is an integer. (i) Explain why $2n-1$ is odd. (ii) Write down the odd number that comes next after $2n-1$. (iii) Show that the difference between the squares of two successive odd numbers is a multiple of $8$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Factorising an expression

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