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.

Answer 1

The answer is 2x because the evasion is (2x)3+(1)3. 3 times 1 is 3. so it is (2x)3+3. you more the 3 next to the 2x over and now it id 2x+3-3.2x

Answer 2

`8x^3+1` is the answer.

Explanation:

Here we know that

`(a+b) (a^2-ab+b^2) = a^3+b^3`

here we have a =2x and b =1

on plugging these values we get

`a^3+b^3=(2x)^3+(1)^3\\8x^3 +1`