What is the factorized form of the polynomial \(121x^2-144\)?
Answer and explanation
Correct answer: \((11x-12)(11x+12)\)
Here, \(121x^2=(11x)^2\) and \(144=12^2\). Therefore, \(121x^2-144=(11x)^2-12^2\). Using the difference-of-squares identity \(a^2-b^2=(a-b)(a+b)\), the factorized form is \((11x-12)(11x+12)\). Options C and D are squares of binomials, so they do not represent this difference. Exam tip: whenever an expression is the difference of two perfect squares, apply \(a^2-b^2=(a-b)(a+b)\).
Frequently asked questions
What is the correct answer to this question?
\((11x-12)(11x+12)\)
Why is this the correct answer?
Here, \(121x^2=(11x)^2\) and \(144=12^2\). Therefore, \(121x^2-144=(11x)^2-12^2\). Using the difference-of-squares identity \(a^2-b^2=(a-b)(a+b)\), the factorized form is \((11x-12)(11x+12)\). Options C and D are squares of binomials, so they do not represent this difference. Exam tip: whenever an expression is the difference of two perfect squares, apply \(a^2-b^2=(a-b)(a+b)\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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