Question

Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = 1.

Which product should Tomas choose?

(2x + 1)(2x2 + 2x – 1)
(2x + 1)(4x3 + 2x – 1)
(2x + 1)(4x2 – 2x + 1)
(2x + 1)(2x2 – 2x + 1)

Answer 1

This is a simple substitution problem. Clearly the answer here is (2x + 1)(4x2 – 2x + 1). We just have to replace a with 2x and b with 1. The tricky part here is the first term in the second group of terms. 2x is to be squared. Common mistake here is raising the x with 2 and not including the coefficient.