Multiply (5x - 1)(5x - 1)

Rationale

(5x - 1)(5x - 1) equals 25x² - 10x + 1.

To expand the expression (5x - 1)(5x - 1), we use the distributive property (also known as the FOIL method for binomials), which results in 25x² - 10x + 1.

A (25x² + 1) YOUR ANSWER

This choice incorrectly suggests that there is no linear term from the multiplication. The correct expansion includes a linear term derived from multiplying the two binomial terms, which results in a negative linear coefficient, not a constant addition.

B (25x² - 1) YOUR ANSWER

This option also fails to account for the linear term that is generated during the expansion. The original expression leads to a quadratic term and a negative linear term, not a constant subtraction of 1.

C (25x² - 2x + 1) YOUR ANSWER

While this option includes the correct quadratic term and a constant, it incorrectly provides a linear term of -2x. The proper expansion yields -10x, not -2x, making this choice incorrect.

D (25x² - 10x + 1) CORRECT

This choice accurately reflects the result of expanding the expression (5x - 1)(5x - 1). The quadratic term is 25x², the linear term is -10x, and the constant term is +1, aligning perfectly with the binomial multiplication.

Conclusion

The expansion of the expression (5x - 1)(5x - 1) correctly results in 25x² - 10x + 1. This showcases the importance of properly applying the distributive property to ensure all terms are accounted for, as incorrect terms can lead to significant errors in polynomial multiplication. The correct answer, D, represents the accurate result, while the other options illustrate common pitfalls in algebraic expansion.

Multiply (5x - 1)(5x - 1)

(5x - 1)(5x - 1) equals 25x² - 10x + 1.

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