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?
A) (2x + 1)(2x2 + 2x – 1)
B) (2x + 1)(4x3 + 2x – 1)
C) (2x + 1)(4x2 – 2x + 1)
D) (2x + 1)(2x2 – 2x + 1)

Answer 1

(a + b) * (a^2 - a*b + b^2)

= (2x + (1)) * ((2x)^2 - (2x)*(1) + (1)^2)

C) (2x + 1) * (4x^2 - 2x + 1)

Answer 2

we know that

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

we are given

`a=2x`

`b=1`

now, we can plug this in formula

and we get

`(2x)^3+(1)^3=(2x+1)((2x)^2-(2x*1)+(1)^2)`

now, we can simplify it

and we get

`(2x)^3+1^3=(2x+1)(4x^2-2x+1)`

so,

option-C.......Answer