Step 1

Given expression is:ac−ad+bd−bc.

ac−ad+bd−bc

On simplifying further we get:

ac−ad+bd−bc=ac−ad−bc+bd

=a(c-d)-b(c-d)

=(c-d)(a-b)

\(\Rightarrow ac−ad+bd−bc=(c−d)(a−b)\)

Alternate:

ac−ad+bd−bc

On simplifying further we get:

ac−ad+bd−bc=ac−bc−ad+bd

=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.

Given expression is:ac−ad+bd−bc.

ac−ad+bd−bc

On simplifying further we get:

ac−ad+bd−bc=ac−ad−bc+bd

=a(c-d)-b(c-d)

=(c-d)(a-b)

\(\Rightarrow ac−ad+bd−bc=(c−d)(a−b)\)

Alternate:

ac−ad+bd−bc

On simplifying further we get:

ac−ad+bd−bc=ac−bc−ad+bd

=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.