What is the value of \( (x+3y)^2-x^2-9y^2-6xy \)?
Answer and explanation
Correct answer: 0
Using \( (a+b)^2=a^2+2ab+b^2 \), with \(a=x\) and \(b=3y\), we get \( (x+3y)^2=x^2+6xy+9y^2 \). Thus, the \(x^2\), \(6xy\), and \(9y^2\) terms all cancel in the given expression, leaving \(0\). \(6xy\) is only the middle term in the expansion, not the final value. Exam tip: always check the middle term \(2ab\) when expanding a square.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
Using \( (a+b)^2=a^2+2ab+b^2 \), with \(a=x\) and \(b=3y\), we get \( (x+3y)^2=x^2+6xy+9y^2 \). Thus, the \(x^2\), \(6xy\), and \(9y^2\) terms all cancel in the given expression, leaving \(0\). \(6xy\) is only the middle term in the expansion, not the final value. Exam tip: always check the middle term \(2ab\) when expanding a square.
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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