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 = y.

Which product should Tomas choose?

(2x + y)(2x2 + 2xy – y2)
(2x + y)(4x2 + 2xy – y2)
(2x + y)(4x2 – 2xy + y2)
(2x + y)(2x2 – 2xy + y2)

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 = y.

Which product should Tomas choose?

(2x + y)(2x2 + 2xy – y2)
(2x + y)(4x2 + 2xy – y2)
(2x + y)(4x2 – 2xy + y2)
(2x + y)(2x2 – 2xy + y2)

snowflake0531 · Answer

We already have that $$a^3+b^3 = (a+b)(a^2 -ab+b^2)$$
So, put in $$a=2x, b=y$$

snowflake0531 · Answer

Substitute the different variables in