A student is asked to factor, if possible, the given expression. The student's response demonstrates which common misconception?

Question

3 years ago

8

Simplify: a2 + b2 Student's response: (a + b)(a − b)

1 answer:

dlinn [17] · Answer 1 · 2022-01-11T10:17:35+03:00

dlinn [17]3 years ago

8 0

Answer:

The student assumed he was asked to factor

(a^2 - b^2)

Which is equal to

= (a+b)*(a-b) (His response)

But, he was asked to simplify

(a^2 + b^2)

Which has imaginary roots, and can be factored as:

(b +ai)(b-ai)