Which of these expressions is equivalent to ac−adf+bc−bdf
?
Responses
(a−b)(c+df)
, open paren A minus b close paren times open paren c plus d f close paren
(a+b)(c+df)
, open paren A plus b close paren times open paren c plus d f close paren
(a−b)(c−df)
open paren A minus b close paren times open paren c minus d f close paren
(a+b)(c−df)
so the bot calculates the correct choice, then denies that it was given as one of the choices. What a loser!
This bot is truly awful. It ought to be banned.
To determine which expression is equivalent to ac − adf + bc − bdf, we can simplify and rearrange the given expression using the distributive property of multiplication over addition and subtraction.
Step 1: Group the terms by their common factors.
a(c - df) + b(c - df)
Step 2: Factor out the common term (c - df).
(c - df)(a + b)
Therefore, the expression (c - df)(a + b) is equivalent to ac − adf + bc − bdf.
None of the given expressions is equivalent to ac−adf+bc−bdf.
We can factor out a common factor of d from the second and fourth terms, and a common factor of c from the first and third terms, to get:
ac - adf + bc - bdf
= (ac + bc) - d(af + bf)
= c(a + b) - d(a + b)f
= (a + b)(c - df)
Therefore, the equivalent expression is (a + b)(c - df), as given in option (d).