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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 (a-b)2 can be explained by using multiplication of binomials as follows:
(a-b)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.
- (a-b)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.
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!CorrectIncorrect