Question

Which of the following is a perfect square trinomial?

A. 4x² + 20xy-252
B. 4x2 + 14xy-252
C. 4x²-20xy + 25,2
OD. 4x2-14xy + 25,²

Answer 1

A perfect square trinomial is a quadratic trinomial that can be factored into the square of a binomial. Options C and D are both perfect square trinomials as they can be factored into the square of (2x - 5).

Step-by-step explanation:

A perfect square trinomial is a quadratic trinomial that can be factored into the square of a binomial. In this case, we need to identify the trinomial that can be written as the product of two identical binomials.

Let's check each option:

1. A. 4x² + 20xy - 252: This trinomial cannot be factored into the square of a binomial because the coefficients of the first and third terms are not perfect squares. It is not a perfect square trinomial.
2. B. 4x² + 14xy - 252: Similar to option A, this trinomial cannot be factored into the square of a binomial because the coefficients of the first and third terms are not perfect squares. It is not a perfect square trinomial.
3. C. 4x² - 20xy + 25: This trinomial can be factored into the square of a binomial: (2x - 5)². It is a perfect square trinomial.
4. D. 4x² - 14xy + 25: Similar to option C, this trinomial can also be factored into the square of a binomial: (2x - 5)². It is a perfect square trinomial.

Therefore, options C and D are both perfect square trinomials.

Learn more about Perfect square trinomials