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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)

Respuesta :

Hagrid
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. 
Eduard22sly

The product that Tomas should choose given that the pattern resulted in a sum of cube is (2x + 1)(4x² – 2x + 1)

Data obtained from the question

  • Polynomial => (a + b)(a² – ab + b²)
  • a = 2x
  • b = 1
  • Product =?

How to determine the product

(a + b)(a² – ab + b²)

But

a = 2x

b = 1

Substituting the value of a and b, we have

(a + b)(a² – ab + b²)

(2x + 1)[(2x)² – (2x × 1) + 1²]

(2x + 1)(4x² – 2x + 1)

Thus, the product that Tomas should choose is (2x + 1)(4x² – 2x + 1)

Learn more about polynomial:

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