What is the value of ( (3x+4)(3x-4)-(9x^2-20) )?
Answer and explanation
Correct answer: (4)
Use the difference-of-squares identity \( (a+b)(a-b)=a^2-b^2\). In the first product, let \(a=3x\) and \(b=4\). Thus, \((3x+4)(3x-4)=(3x)^2-4^2=9x^2-16\). The full expression is then \((9x^2-16)-(9x^2-20)\). Distribute the minus sign across the second bracket: \(9x^2-16-9x^2+20\). The x-squared terms cancel and the constants give \(-16+20=4\). Therefore, option A is correct.
A common error is to subtract only the first term inside the second bracket and leave its constant unchanged. The minus sign applies to both terms, so \(-(9x^2-20)=-9x^2+20\). Directly simplifying the two brackets shows the same result: the first is \(9x^2-16\), and after subtraction the variable terms disappear. Since no value of x is specified, the result must be the constant 4, not an expression depending on x.
Frequently asked questions
What is the correct answer to this question?
(4)
Why is this the correct answer?
Use the difference-of-squares identity \( (a+b)(a-b)=a^2-b^2\). In the first product, let \(a=3x\) and \(b=4\). Thus, \((3x+4)(3x-4)=(3x)^2-4^2=9x^2-16\). The full expression is then \((9x^2-16)-(9x^2-20)\). Distribute the minus sign across the second bracket: \(9x^2-16-9x^2+20\). The x-squared terms cancel and the constants give \(-16+20=4\). Therefore, option A is correct.
A common error is to subtract only the first term inside the second bracket and leave its constant unchanged. The minus sign applies to both terms, so \(-(9x^2-20)=-9x^2+20\). Directly simplifying the two brackets shows the same result: the first is \(9x^2-16\), and after subtraction the variable terms disappear. Since no value of x is specified, the result must be the constant 4, not an expression depending on x.
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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