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

Lennie Carroll

Lennie Carroll

Answered question

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.

Answer & Explanation

Cristiano Sears

Cristiano Sears

Skilled2021-05-15Added 96 answers

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)
acad+bdbc=(cd)(ab)
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)
acad+bdbc=(cd)(ab)
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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