What is the simplified form of ( (x+2)(x+6)-(x+3)(x+5) )?
Answer and explanation
Correct answer: -3
\((x+2)(x+6)=x^2+8x+12\) and \((x+3)(x+5)=x^2+8x+15\). Hence, their difference is \((x^2+8x+12)-(x^2+8x+15)=-3\). Option 3 is incorrect because the \(x^2\) and \(8x\) terms cancel, so no term containing x remains. Exam tip: while subtracting an expression in brackets, change the sign of every term in the second bracket.
Frequently asked questions
What is the correct answer to this question?
-3
Why is this the correct answer?
\((x+2)(x+6)=x^2+8x+12\) and \((x+3)(x+5)=x^2+8x+15\). Hence, their difference is \((x^2+8x+12)-(x^2+8x+15)=-3\). Option 3 is incorrect because the \(x^2\) and \(8x\) terms cancel, so no term containing x remains. Exam tip: while subtracting an expression in brackets, change the sign of every term in the second bracket.
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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