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 = 1Which product should Tomas choose?

Answer 1

I got the answer 8x^3+1 by putting the values in the above formula

Answer 2

Answer with explanation:

Product Rule learned by Thomas

 $a^3 +b^3=(a+b)(a^2-ab+b^2)$

Now we have to find the value of

 $(2 x)^3 +1^3\\\\=8x^3+1\\\\=(2 x+1)[(2x)^2-2 \times 2x \times 1 +1^2]\\\\=(2 x+1)[4x^2-4 x +1]$

The product that Thomas should choose

 =(2 x+1)(4 x²-4 x+1)