Kylie explained that (-4x + 9)² will result in a difference of squares because (-4x + 9)² = (-4x)² - (9)² = 16x² - 81. Which statement best describes Kylie's explanation?

Question image

Understand the Problem

The question is asking for an evaluation of Kylie's explanation regarding the mathematical expression (-4x + 9)². We need to determine which of the provided statements best describes her understanding and correctness about it resulting in a difference of squares.

Answer

Kylie did not understand that this is a perfect square trinomial.
Answer for screen readers

Kylie did not understand that this is a perfect square trinomial.

Steps to Solve

  1. Identify the Expression and Its Meaning

The expression given is $(-4x + 9)^2$. This is not a difference of squares but rather a perfect square trinomial.

  1. Understand Perfect Square Trinomials

A perfect square trinomial can be expressed as $(a + b)^2 = a^2 + 2ab + b^2$. In our case, $a = -4x$ and $b = 9$.

  1. Expand the Perfect Square Trinomial

Using the formula for a perfect square trinomial, we expand: $$ (-4x + 9)^2 = (-4x)^2 + 2(-4x)(9) + 9^2 $$ Calculating each part:

  • $(-4x)^2 = 16x^2$
  • $2(-4x)(9) = -72x$
  • $9^2 = 81$

Combining these gives: $$ 16x^2 - 72x + 81 $$

  1. Conclusion on Kylie's Explanation

Kylie claimed that $(-4x + 9)^2$ results in a difference of squares, which is incorrect. It is a perfect square trinomial.

Kylie did not understand that this is a perfect square trinomial.

More Information

Kylie's mistake lies in misclassifying the expression. A difference of squares takes the form $a^2 - b^2$, which is clearly not applicable here since $(-4x + 9)^2$ is a perfect square.

Tips

  • Confusing perfect square trinomials with differences of squares.
  • Not applying the correct formula for binomial squares.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!
Use Quizgecko on...
Browser
Browser