Consider the expressions (x-4) (3x-6) and 3x^2-18x+24. Show that the two expressions define the same function

see explanation

Step-by-step explanation:

Expand the factors

(x - 4) (3x - 6)

Each term in the second factor is multiplied by each term in the first factor, that is

x (3x - 6) - 4 (3x - 6) ← distribute both parenthesis

= 3x² - 6x - 12x + 24 ← collect like terms

= 3x² - 18x + 24 ← this is the other function

Thus both expressions define the same function