(ax+b)(cx+d): Error Analysis & Misconceptions
Mathematics
Grade 8
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on expanding the product (ax+b)(cx+d), addressing common misconceptions and errors. Suitable for Grade 8 students to develop procedural mastery and reasoning skills.
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Full preview • 14 questions
(ax+b)(cx+d): 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 (2x + 3)(x + 4) and simplify your answer.
[3 marks]2.
Determine the expanded form of (5x - 2)(3x + 7).
[3 marks]3.
If (ax + b)(cx + d) = 6x^2 + 13x + 8, find possible values of a, b, c, and d.
[4 marks]4.
Construct the expansion of (x + 5)(x + 2) using the grid to show each step.
[4 marks]B
Problem Solving & Reasoning
Answer carefully, explaining your reasoning where required.
1.
A rectangle's length is represented by (3x + 2), and its width by (x + 4). Write an expression for the area and expand it.
[4 marks]2.
Identify and correct the mistake in the expansion: (4x + 5)(x + 3) = 4x^2 + 15x + 15.
[4 marks]3.
If (ax + b)(cx + d) = 12x^2 + 7x + 10, find possible values of a, b, c, and d, and justify your answer.
[4 marks]4.
Explain why the expansion of (x + 3)(x + 3) is different from (x + 3)^2, and expand both to show.
[4 marks]C
Real-world Applications
Solve these word problems using your expanding skills.
1.
A company is designing a rectangular garden. The length is represented by (x + 2), and the width by (2x + 3). Write an expression for the area, expand it, and determine the area when x=4.
[4 marks]D
Challenge & Extension
Attempt these more advanced problems to extend your understanding.
1.
Given that (ax + b)(cx + d) = 6x^2 + 11x + 10, find integer values of a, b, c, and d that satisfy the conditions, and explain your reasoning.
[4 marks]2.
Prove that expanding (ax + b)(cx + d) always results in a quadratic expression, and identify the coefficients in terms of a, b, c, and d.
[4 marks]E
Mixed Review & Error Analysis
Identify and correct the errors in the following expansions.
1.
Error! Expand (3x + 4)(x + 5) and identify the mistake in the expansion: 3x^2 + 20x + 20.
[4 marks]2.
A student expanded (x + 2)(x + 3) as x^2 + 5x + 6. Is this correct? Justify your answer.
[2 marks]3.
Identify the mistake in: (2x - 3)(x + 4) = 2x^2 + 4x - 3x - 12.
[2 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet