If the final area of a square of side (q-4) is needed, which expansion is correct?
Answer and explanation
Correct answer: \(q^2-8q+16\)
The area of a square is the square of its side, so the area is \((q-4)^2\). Using \((a-b)^2=a^2-2ab+b^2\), with \(a=q\) and \(b=4\), gives \(q^2-2\times q\times4+16=q^2-8q+16\). In option A, the factor 2 is missing from the middle term. Exam tip: the middle term in \((a-b)^2\) is always negative, \(-2ab\).
Frequently asked questions
What is the correct answer to this question?
\(q^2-8q+16\)
Why is this the correct answer?
The area of a square is the square of its side, so the area is \((q-4)^2\). Using \((a-b)^2=a^2-2ab+b^2\), with \(a=q\) and \(b=4\), gives \(q^2-2\times q\times4+16=q^2-8q+16\). In option A, the factor 2 is missing from the middle term. Exam tip: the middle term in \((a-b)^2\) is always negative, \(-2ab\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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