Which polynomial is a difference of two squares? x² + 25 and x² - 25

Soltion:

We will use the algebraic identity a²- b² = (a + b)(a - b) which is also known as the difference of two squares.

Let us see how we will use the concept of factoring polynomials that are used to express the differences between two perfect squares.

Given: The polynomials x² + 25 and x² - 25

The difference of two squares or a²- b² formula is a formula that helps us express a quadratic polynomial as a product of two binomials where one shows the sum and the other shows the difference of the two perfect squares respectively.

The formula is a²-b² = (a + b)(a - b)

x² - 25 can be rewritten as x² - 5² 

On multiplying (x + 5)(x - 5), we get x² + 5x - 5x - 25 =  x² - 25.

Thus the polynomial that is the difference of two squares is x² - 25.

Which polynomial is a difference of two squares? x² + 25 and x² - 25

Summary:

The polynomial that is the difference of two squares is x² - 25.