Special Algebraic Identities 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 special algebraic identities free

What this topic covers

Worked examples

Example 1

Expand (2x+8)(2x−8)(2x + 8)(2x - 8).
Show the worked solution
  • $(2x + 8)(2x - 8) = (2x)^2 - 8^2 \quad \scriptsize\textit{difference of two squares}$
  • $= 4x^2 - 64$
  • $= 4x^2-64$

Answer: 4x2−644x^2-64

Example 2

Factorise 16x2−9y216x^2 - 9y^2.
Show the worked solution
  • Recognise the difference of two squares pattern: $a^2 - b^2 = (a + b)(a - b)$.
  • Here $a = 4x$ and $b = 3y$, since $(4x)^2 = 16x^2$ and $(3y)^2 = 9y^2$.
  • $16x^2 - 9y^2 = (4x + 3y)(4x - 3y)$

Answer: (4x+3y)(4x−3y)(4x+3y)(4x-3y)

Example 3

Evaluate 2032−9203^2 - 9 without a calculator.
Show the worked solution
  • Recognise $9 = 3^2$, so apply the difference of two squares:
  • $203^2 - 9 = 203^2 - 3^2$
  • $= (203 + 3)(203 - 3) \quad \scriptsize\textit{difference of two squares}$
  • $= 206 \times 200$
  • $= 41200$

Answer: 4120041200

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.

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