Question

Which trinomial is equivalent to 3(x-2)^2 - 2(x-1)

Answer 1

This expression can be simplified so it becomes:

(3x^2 - 4) - (2x - 1)

3x^2 - 2x - 3

Answer 2

`3x^2-14x+14`

Explanation:

the expression we have is:

`3(x-2)^2-2(x-1)`

to solve we need to develop the square binomial

`(x-2)^2`

with the following formula:

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

So we have:

`(x-2)^2=x^2-2*2x+2^2\\(x-2)^2=x^2-4x+4`

and the expression now is:

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

developing multiplications to remove parentheses:

`3x^2-3*4x+3*4-2x+2*1\\3x^2-12x+12-2x+2`

joining like terms:

`3x^2-14x+14`