Expansion and Factorisation practice questions

Secondary 2 topics, working towards the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise expansion and factorisation free

What this topic covers

Worked examples

Example 1

Expand (x−6)(2x−5)(x - 6)(2x - 5).
Show the worked solution
  • $(x - 6)(2x - 5)$
  • $= 2x^2 - 5x - 12x + 30 \quad \scriptsize\textit{expand}$
  • $= 2x^2 - 17x + 30$
  • $= 2x^2-17x+30$

Answer: 2x2−17x+302x^2-17x+30

Example 2

Factorise x2+x−20x^2 + x - 20.
Show the worked solution
  • Find two numbers whose product is $-20$ and sum is $1$.
  • The numbers are $5$ and $-4$ since $5 \times (-4) = -20$ and $5 + (-4) = 1$.
  • $x^2 + x - 20 = (x + 5)(x - 4)$

Answer: (x+5)(x−4)(x+5)(x-4)

Example 3

Factorise 9ax+12at+12nx+16nt9ax + 12at + 12nx + 16nt.
Show the worked solution
  • $9ax + 12at + 12nx + 16nt$
  • $= (9ax + 12at) + (12nx + 16nt) \quad \scriptsize\textit{group}$
  • $= 3a(3x + 4t) + 4n(3x + 4t) \quad \scriptsize\textit{extract common factors}$
  • $= (3a+4n)(3x+4t)$

Answer: (3a+4n)(3x+4t)(3a+4n)(3x+4t)

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

Other Secondary 2 topics