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Correct Response: Option B
Around 50% of the teachers chose the right option. Around 20% of teachers chose option C and D each.
This question tests for teacher’s knowledge of pedagogical sequence of topics in order to remediate misconceptions in students.
The expansion of the identity (ab)2 can be explained by using multiplication of binomials as follows:
(ab)2 = (a – b) x (a – b)
= a x (a – b) – b x (a – b)
= (a x a) – (a x b) – (b x a) + (b x b)
= a2 – 2ab + b2
Hence, Option B is the correct answer.
 (ab)2 expansion involves addition of two negative terms. Also, subtraction of polynomials does not help explain how b2 has a positive sign instead of a negative sign. Hence, option A is incorrect.
 The students might have applied the distributive property incorrectly to arrive at a2 – b2 by using the logic that the square of (a – b) is equal to sum of the square of the terms inside. Distributive property is just a part of the procedural expansion of multiplication of binomials. Hence, it won’t help resolve the misconception.
 The laws of exponents are used to simplify powers of numbers with same bases where they are multiplied or divided. This can’t be used to explain the identity. Hence, Option D is incorrect.
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1. Question
This is a CENTA TPO Question related to the CENTA Standard ‘Student Assessment and Remediation – Remediation and Communication’ –
Question: 70% of the class writes the expansion of ‘(a – b)2’ as ‘a2 – b2’
Which of the following topics would be MOST important for the teacher to take up, to address the misconception?
Note: Don’t forget to finish the Quiz and find the explanation for the right answer!
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