Answer :
Let's see what the options look like when we multiply the expressions in brackets:
(first, i multiply both parts of the second bracked by the first part of the first bracket, and then the same with the second part of the first bracket:
(1) (3x - 3)(x - 2))
3x2 +6x -3x +6// this is not correct
(2) (3x + 3)(x - 2)
3x2-6x+3x-6//this is not correct
(3)
3(x + 1)(x - 2)
3(x2-2x+x-2)//simplifying:
3(x2-x-2)//multiplying:
3x2-3x-6)
- so this is not correct either
(4) 3(x - 1)(x - 2)
3(x2-2x - x + 2)
3(x2-3x +2)
3x2-9x +6 - well, here is our winner!
(first, i multiply both parts of the second bracked by the first part of the first bracket, and then the same with the second part of the first bracket:
(1) (3x - 3)(x - 2))
3x2 +6x -3x +6// this is not correct
(2) (3x + 3)(x - 2)
3x2-6x+3x-6//this is not correct
(3)
3(x + 1)(x - 2)
3(x2-2x+x-2)//simplifying:
3(x2-x-2)//multiplying:
3x2-3x-6)
- so this is not correct either
(4) 3(x - 1)(x - 2)
3(x2-2x - x + 2)
3(x2-3x +2)
3x2-9x +6 - well, here is our winner!
3x² - 9x + 6
3(x²) - 3(3x) + 3(2)
3(x² - 3x + 2)
3(x² - 2x - x + 2)
3(x(x) - x(2) - 1(x) + 1(2))
3(x(x - 2) - 1(x - 2))
3(x - 1)(x - 2)
The equation 3x² - 9x + 6 is equivalent to 3(x - 1)(x - 2).
3(x²) - 3(3x) + 3(2)
3(x² - 3x + 2)
3(x² - 2x - x + 2)
3(x(x) - x(2) - 1(x) + 1(2))
3(x(x - 2) - 1(x - 2))
3(x - 1)(x - 2)
The equation 3x² - 9x + 6 is equivalent to 3(x - 1)(x - 2).
