Question

Which of the following is the perfect square of a binomial?

A. x² + y²
B. 25x² - 100
C. x² - 3xy + 9y²
D. x² + 2xy² + y⁴

Answer 1

The perfect square of a binomial is an expression that can be written as (a + b)² or (a - b)². Out of the given options, B. 25x² - 100 and D. x² + 2xy² + y⁴ can be expressed as perfect squares of binomials.

Step-by-step explanation:

The perfect square of a binomial is an expression of the form (a + b)² or (a - b)², where a and b are real numbers. To determine which of the given options is a perfect square of a binomial, we need to identify if the expression can be written in the form (a + b)² or (a - b)². Let's go through each option:

1. A. x² + y²: This is not a perfect square of a binomial because it cannot be written in the form (a + b)² or (a - b)².
2. B. 25x² - 100: This is a perfect square of a binomial. It can be written as (5x)² - 10².
3. C. x² - 3xy + 9y²: This is not a perfect square of a binomial because it cannot be written in the form (a + b)² or (a - b)².
4. D. x² + 2xy² + y⁴: This is a perfect square of a binomial. It can be written as (x + y²)².

Therefore, the correct answer is B. 25x² - 100 and D. x² + 2xy² + y⁴ as they can be expressed as perfect squares of binomials.