Factorise (ab-ac+db-dc) by grouping.
Answer and explanation
Correct answer: \((a+d)(b-c)\)
Group the expression as \(ab-ac+db-dc=a(b-c)+d(b-c)\). The common binomial factor is \((b-c)\), so the factorised form is \((b-c)(a+d)=(a+d)(b-c)\). Expanding option B gives \(ab+ac-db-dc\), which is different from the given expression. Exam tip: expand the factorised form once to check the signs.
Frequently asked questions
What is the correct answer to this question?
\((a+d)(b-c)\)
Why is this the correct answer?
Group the expression as \(ab-ac+db-dc=a(b-c)+d(b-c)\). The common binomial factor is \((b-c)\), so the factorised form is \((b-c)(a+d)=(a+d)(b-c)\). Expanding option B gives \(ab+ac-db-dc\), which is different from the given expression. Exam tip: expand the factorised form once to check the signs.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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