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Bunuel
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Bunuel
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This is a very good question Bunuel

1 doubt - How can we understand that this question could be manipulated to the form (a-b)^2 at the first instance? Is this manipulation is something that comes by practice or is there any methodology or tips do you have to easily identify this?

Thanks a lot in advance!
Bunuel
Official Solution:

\(-0.05 + 0.000025 + 25 = \)

A. \(4.995^2\)
B. \(4.95^2\)
C. \(4.5^2\)
D. \(-4.95^2\)
E. \(-4.995^2\)


Recognize that we have the square of the difference:

\(-0.05 + 0.000025 + 25 = \)

\(=-2*0.005*5 + 0.005^2+5^2=\)

\(=(0.005 - 5)^2=\)

\(=4.995^2\)


Answer: A

Understanding how to manipulate an expression often comes with practice and familiarity with algebraic identities. Recognizing patterns like these becomes easier as you work through different types of algebraic problems. There isn’t a strict method to follow, but here are a few tips:

  • The numbers 0.000025 and 25 are both squares: 0.000025 is the square of 0.005, and 25 is the square of 5. This should immediately suggest a relationship involving squared terms.
  • The options are all squares: Since all the answer choices involve squared numbers, this further indicates that the problem is likely related to a squared expression.

Together, these clues hint that the expression is likely in a form like (a - b)^2 or (a + b)^2, helping you quickly identify the pattern and solve the problem.
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I did not quite understand the solution. Hello - How did (0.005 - 5)^2 become 4.995^2? Shouldn't it be -4.995^2? Or am I missing something simple?
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I did not quite understand the solution. Hello - How did (0.005 - 5)^2 become 4.995^2? Shouldn't it be -4.995^2? Or am I missing something simple?

You're missing something important: brackets matter.

(0.005 - 5)^2 simplifies to (-4.995)^2, which equals 4.995^2 because squaring a negative number results in a positive value.

However, -4.995^2 (without brackets) means -(4.995^2), which is a negative number. The correct interpretation here is (-4.995)^2, not -4.995^2.

This distinction is key, as the presence of brackets changes the meaning entirely.
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