Write ( x^2-49 ) in factors.
Answer and explanation
Correct answer: \((x-7)(x+7)\)
Use the identity \(a^2-b^2=(a-b)(a+b)\). Since \(49=7^2\), \(x^2-49=x^2-7^2=(x-7)(x+7)\). The close distractor \((x-7)^2\) expands to \(x^2-14x+49\), so it is not equal to the given expression. Exam tip: find the square root of the constant term before applying the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
\((x-7)(x+7)\)
Why is this the correct answer?
Use the identity \(a^2-b^2=(a-b)(a+b)\). Since \(49=7^2\), \(x^2-49=x^2-7^2=(x-7)(x+7)\). The close distractor \((x-7)^2\) expands to \(x^2-14x+49\), so it is not equal to the given expression. Exam tip: find the square root of the constant term before applying the difference-of-squares identity.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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