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Expansion and Factorisation of Algebraic Expressions

Secondary 2 practice

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Expansion and Factorisation of Algebraic Expressions 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 of Algebraic Expressions free

What this topic covers

Worked examples

Example 1

Expand (2x+2)(2x−2)(2x + 2)(2x - 2).
Show the worked solution
  • (2x+2)(2x−2)(2x + 2)(2x - 2)
  • =4x2−4x+4x−4expand= 4x^2 - 4x + 4x - 4 \quad \scriptsize\textit{expand}
  • =4x2−4= 4x^2 - 4

Answer: 4x2−44x^2-4

Example 2

Factorise x2−18x+81x^2 - 18x + 81.
Show the worked solution
  • Find two numbers whose product is 8181 and sum is −18-18.
  • The numbers are −9-9 and −9-9 since (−9)×(−9)=81(-9) \times (-9) = 81 and (−9)+(−9)=−18(-9) + (-9) = -18.
  • x2−18x+81=(x−9)(x−9)x^2 - 18x + 81 = (x - 9)(x - 9)
  • =(x−9)2= (x - 9)^2

Answer: (x−9)(x−9)(x-9)(x-9)

Example 3

Factorise 16mx+12my−20bx−15by16mx + 12my - 20bx - 15by.
Show the worked solution
  • 16mx+12my−20bx−15by16mx + 12my - 20bx - 15by
  • =(16mx+12my)−(20bx+15by)group= (16mx + 12my) - (20bx + 15by) \quad \scriptsize\textit{group}
  • =4m(4x+3y)−5b(4x+3y)extract common factors= 4m(4x + 3y) - 5b(4x + 3y) \quad \scriptsize\textit{extract common factors}
  • =(4m−5b)(4x+3y)= (4m-5b)(4x+3y)

Answer: (4m−5b)(4x+3y)(4m-5b)(4x+3y)

Questions parents ask

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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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