Question

# Use two different groupings to factor ac-ad+bd-bc in two ways. Then explain why the two factorizations are the same.

Polynomial factorization
Use two different groupings to factor ac-ad+bd-bc in two ways. Then explain why the two factorizations are the same.

2021-05-15
Step 1
On simplifying further we get:
=a(c-d)-b(c-d)
=(c-d)(a-b)
$$\Rightarrow ac−ad+bd−bc=(c−d)(a−b)$$
Alternate:
On simplifying further we get:
=c(a-b)-d(a-b)
=(a-b)(c-d)
$$\Rightarrow ac−ad+bd−bc=(c−d)(a−b)$$
Step 2
The two factorizations are same, because the factors of an expression are always same irrespective of how we simplify the expression in factorized form.