Question

What is the factored form of n^2 - 25?

a) (n - 25)(n - 1)
b) (n - 5)(n + 5)
c) (n + 5)(n + 5)
d) (n - 5)(n - 5)

Answer 1

The factored form of n^2 - 25 is (n - 5)(n + 5), which is a difference of squares where n is the variable and 5 is the square root of 25.

Step-by-step explanation:

The factored form of n^2 - 25 is a difference of squares. In this situation, we are trying to factorize an expression where one term is the square of a variable (n^2) and the other is a square of a constant (25).

To factor a difference of squares, we look for two terms (a and b) such that:

• a^2 - b^2 = (a - b)(a + b).

In the case of n^2 - 25, we recognize that:

• a = n
• b = 5,

since 5^2 = 25. Plugging these into the difference of squares formula, we get:

• (n - 5)(n + 5),

Therefore, the factored form of n^2 - 25 is (n - 5)(n + 5), which corresponds to option b).