What is the expansion of \\((5x+2)^2\\)?
Answer and explanation
Correct answer: \\(25x^2+20x+4\\)
Use the identity \\((a+b)^2=a^2+2ab+b^2\\). Here, \\(a=5x\\) and \\(b=2\\). Thus, \\(a^2=25x^2\\), \\(2ab=2\\cdot5x\\cdot2=20x\\), and \\(b^2=4\\). Therefore, the expansion is \\(25x^2+20x+4\\). Option B incorrectly gives the middle term as \\(10x\\) by missing the factor 2. In an exam, check the middle term using \\(2ab\\).
Frequently asked questions
What is the correct answer to this question?
\\(25x^2+20x+4\\)
Why is this the correct answer?
Use the identity \\((a+b)^2=a^2+2ab+b^2\\). Here, \\(a=5x\\) and \\(b=2\\). Thus, \\(a^2=25x^2\\), \\(2ab=2\\cdot5x\\cdot2=20x\\), and \\(b^2=4\\). Therefore, the expansion is \\(25x^2+20x+4\\). Option B incorrectly gives the middle term as \\(10x\\) by missing the factor 2. In an exam, check the middle term using \\(2ab\\).
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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