What is the value of \(3.5^2-2.5^2\)?
Answer and explanation
Correct answer: 6
Use the difference-of-squares identity \(a^2-b^2=(a-b)(a+b)\), which is valid for real numbers, including decimals. Here \(a=3.5\) and \(b=2.5\). Thus \(3.5^2-2.5^2=(3.5-2.5)(3.5+2.5)=1\times6=6\). A direct check gives \(3.5^2=12.25\) and \(2.5^2=6.25\), and \(12.25-6.25=6\), confirming the result. Therefore option B is correct. Option A confuses the difference with one of the factors, while options C and D arise from incorrect addition or squaring. Factoring is especially efficient here because the two numbers differ by exactly 1.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Use the difference-of-squares identity \(a^2-b^2=(a-b)(a+b)\), which is valid for real numbers, including decimals. Here \(a=3.5\) and \(b=2.5\). Thus \(3.5^2-2.5^2=(3.5-2.5)(3.5+2.5)=1\times6=6\). A direct check gives \(3.5^2=12.25\) and \(2.5^2=6.25\), and \(12.25-6.25=6\), confirming the result. Therefore option B is correct. Option A confuses the difference with one of the factors, while options C and D arise from incorrect addition or squaring. Factoring is especially efficient here because the two numbers differ by exactly 1.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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