(x+a)(x+b): Error Analysis & Misconceptions
Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding, applying, and correcting errors related to expanding (x + a)(x + b). It includes practice, reasoning, real-world contexts, and extension problems.
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(x+a)(x+b): Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Expand the expression (x + 3)(x + 5) using the FOIL method.
[2 marks]2.
What is the product of (x - 2)(x + 4)?
[2 marks]3.
Expand (x + a)(x + b) where a=2 and b=7. Write your answer in standard form.
[2 marks]B
Error Analysis & Misconceptions
Study the common mistakes shown below. Identify what is wrong and correct the errors.
1.
Student's Work: (x + 4)(x + 6) = x^2 + 24.
Identify the mistake and provide the correct expansion.
[3 marks]2.
A student expands (x + 1)(x + 3) as x^2 + 3x + 1. What is the error? Fix it.
[3 marks]C
Problem Solving & Reasoning
Solve the following problems and explain your reasoning.
1.
If (x + a)(x + b) = x^2 + (a + b)x + ab, explain why this is true for all real numbers a and b.
[4 marks]2.
Solve for x: (x + 2)(x + 4) = 0. Show your working.
[3 marks]D
Real-world Applications
Apply your knowledge to the following word problems.
1.
A rectangular garden has sides of length (x + 3) meters and (x + 5) meters. Write an expression for its area and expand it.
[3 marks]E
Challenge & Extension
Tackle these advanced problems to extend your understanding.
1.
Expand (x + a)(x + b) and then factor the resulting quadratic expression. Discuss the conditions under which it can be factored easily.
[4 marks]F
Mixed Review
Answer a variety of questions to review your understanding.
1.
Rewrite the expansion of (x + 1)(x + 2) in standard form.
[2 marks]2.
Identify the error in expanding (x + 2)(x + 3) as x^2 + 6x + 5.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
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- • Add more questions (10 → 15)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet