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 minus b close paren times open paren c minus d f close paren
(a+b)(c−df)
, open paren A plus b close paren times open paren c minus d f close paren
(a+b)(c+df)
AAAaannndd the bot gets it wrong yet again!
can't even tell when it has the right answer!
sure looks like C to me.
The expression that is equivalent to ac−adf+bc−bdf is (a−b)(c−df).
To determine which expression is equivalent to ac−adf+bc−bdf, we can simplify the given expression step by step.
Step 1: Factor out common terms
ac−adf+bc−bdf = (ac + bc) - (adf + bdf)
Step 2: Factor out common factors in each group
(ac + bc) - (adf + bdf) = a(c + b) - df(ad + bd)
Step 3: Further simplify
a(c + b) - df(ad + bd) = a(c + b) - df(a + b)d
From the above steps, it is clear that the correct equivalent expression is (a+c)(c+b) or option (a+b)(c−df).
None of the above expressions is equivalent to ac−adf+bc−bdf.
To simplify the expression ac−adf+bc−bdf, we can factor out a common factor of d from the second and fourth terms:
ac - adf + bc - bdf = ac + bc - adf - bdf = (a+b)c - d(a+b)f
Now, we can factor out a common factor of (a+b) from the first two terms and the last two terms:
(a+b)c - d(a+b)f = (a+b)(c-df)
Therefore, the equivalent expression is (a+b)(c-df).