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)

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)

anonymous · Answer

@FLAMER123 @AlexandervonHumboldt2 @Nnesha @Michele_Laino

watchmath · Answer

Just substitute a=2x and b=1 and see what happens

anonymous · Answer

The first prathesis should be cubed

anonymous · Answer

the formula is (a^3+b^3)(a2-ab+b2)

anonymous · Answer

But the last one is the answer....

watchmath · Answer

the last one is not correct.
The formula is $(a+b)(a^2-ab+b^2)=a^3+b^3$
What do we get if we substitute a=2x and b=1?