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Expansion and Factorisation using Special Algebraic Identities

Secondary 2 practice

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Expansion and Factorisation using 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 Expansion and Factorisation using Special Algebraic Identities free

What this topic covers

Worked examples

Example 1

Expand (3x−2)2(3x - 2)^2.
Show the worked solution
  • (3x−2)2=(3x)2−2(3x)(2)+22perfect square(3x - 2)^2 = (3x)^2 - 2(3x)(2) + 2^2 \quad \scriptsize\textit{perfect square}
  • =9x2−12x+4= 9x^2 - 12x + 4

Answer: 9x2−12x+49x^2-12x+4

Example 2

Factorise 25x2+40x+1625x^2 + 40x + 16.
Show the worked solution
  • Recognise the perfect square trinomial pattern: a2+2ab+b2=(a+b)2a^2 + 2ab + b^2 = (a + b)^2.
  • Take square roots of the first and last terms: 25x2=5x\sqrt{25x^2} = 5x and 16=4\sqrt{16} = 4.
  • Check the middle term: 2×5x×4=40x✓2 \times 5x \times 4 = 40x \checkmark
  • 25x2+40x+16=(5x+4)225x^2 + 40x + 16 = (5x + 4)^2

Answer: (5x+4)2(5x+4)^2

Example 3

Evaluate 205×195205 \times 195 without a calculator.
Show the worked solution
  • Express as (200+5)(200−5)(200 + 5)(200 - 5):
  • 205×195=(200+5)(200−5)205 \times 195 = (200 + 5)(200 - 5)
  • =2002−52difference of two squares= 200^2 - 5^2 \quad \scriptsize\textit{difference of two squares}
  • =40 000−25= 40\,000 - 25
  • =39 975= 39\,975

Answer: 3997539975

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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