Which polynomial is a difference of two squares? x2 + 25 and x2 - 25
We will use the algebraic identity a2- b2 = (a+b)(a-b) which is also known as the difference of two squares.
Answer: The polynomial that is the difference of two squares is x2 - 25.
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.