What is the value of ( (2x+7)^2+(2x-1)^2-2(2x+7)(2x-1) )?
Answer and explanation
Correct answer: 64
The expression has the form \(a^2+b^2-2ab=(a-b)^2\), where \(a=2x+7\) and \(b=2x-1\). Thus, \(a-b=(2x+7)-(2x-1)=8\), so the value is \(8^2=64\). Option 8 is only the difference \(a-b\), not its square. Exam tip: first identify the \(a^2+b^2-2ab\) pattern, then square the difference.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
The expression has the form \(a^2+b^2-2ab=(a-b)^2\), where \(a=2x+7\) and \(b=2x-1\). Thus, \(a-b=(2x+7)-(2x-1)=8\), so the value is \(8^2=64\). Option 8 is only the difference \(a-b\), not its square. Exam tip: first identify the \(a^2+b^2-2ab\) pattern, then square the difference.
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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