Question 27

25x² - 10x + 1

When multiplying the expression (5x - 1)(5x - 1), we apply the distributive property, leading us to 25x² - 10x + 1, which is a perfect square trinomial.

A) 25x² + 1

This option is incorrect because it fails to include the middle term that arises from the multiplication process. The correct expansion results in a negative middle term, which this choice does not account for.

B) 25x² - 1

This choice is also incorrect as it overlooks the necessary middle term. The multiplication of the binomials produces a constant term of +1, not -1, making this option invalid.

C) 25x² - 2x + 1

While this option includes the correct constant term of +1, it incorrectly states the coefficient of the middle term. The accurate result from the expansion should have a middle term of -10x, not -2x.

D) 25x² - 10x + 1

This option correctly represents the expanded form of (5x - 1)(5x - 1), as it includes the correct coefficients for all terms resulting from the multiplication.

Conclusion

Option D is definitively the correct answer as it accurately reflects the result of multiplying the given binomials. All other options either misrepresent the middle term or the constant term, failing to capture the correct expansion. Thus, D stands as the only valid expression for the multiplication of (5x - 1)(5x - 1).