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
ANSWERED
asked 2021-05-14
Use two different groupings to factor ac-ad+bd-bc in two ways. Then explain why the two factorizations are the same.

Answers (1)

2021-05-15
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.
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