If \(27 \times 33\) is treated as ((30-3)(30+3)) in a visual model, what is the area?
Answer and explanation
Correct answer: 891
The numbers 27 and 33 are equally spaced, by 3, on either side of 30. Using \((a-b)(a+b)=a^2-b^2\), \((30-3)(30+3)=30^2-3^2=900-9=891\). The value 900 is only \(30^2\); it does not account for subtracting \(3^2\). Exam tip: when two numbers are equally distant from a middle number, use the difference-of-squares identity for quick multiplication.
Frequently asked questions
What is the correct answer to this question?
891
Why is this the correct answer?
The numbers 27 and 33 are equally spaced, by 3, on either side of 30. Using \((a-b)(a+b)=a^2-b^2\), \((30-3)(30+3)=30^2-3^2=900-9=891\). The value 900 is only \(30^2\); it does not account for subtracting \(3^2\). Exam tip: when two numbers are equally distant from a middle number, use the difference-of-squares identity for quick multiplication.
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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