Question

What is the factored form of a² - 121?

A) (a - 11)(a + 11)
B) (a - 121)(a + 1)
C) (a - 11)(a - 11)
D) (a + 11)(a + 11)

Answer 1

The factored form of a² - 121 is (a - 11)(a + 11), because 121 is the square of 11 and the expression is a difference of squares which factors into (a + 11)(a - 11). option A is correct answer.

Step-by-step explanation:

The factored form of the expression a² - 121 can be determined by recognizing that it is a difference of squares. A difference of squares is a binomial of the form x² - y², which can be factored into the product of the sum and difference of the square roots of the individual terms: (x + y)(x - y).

In this case, the expression can be factored as (a - 11)(a + 11), because 121 is the square of 11, and when we substitute into the formula, a² - 121 = a² - (11²) which factors as (a + 11)(a - 11).

Therefore, the correct answer to the question 'What is the factored form of a² - 121?' is Option A) (a - 11)(a + 11). This is because this set of binomials when multiplied will give the original quadratic expression a² - 121.

Answer 2

The factored form of a² - 121 is (a - 11)(a + 11), which is the application of the difference of squares formula. The correct option given the choices is A) (a - 11)(a + 11).

Step-by-step explanation:

The factored form of a² - 121 is achieved by recognizing that the expression is a difference of squares. The difference of squares formula is a² - b² = (a - b)(a + b). In this case, 121 is a perfect square since it is equal to 11², therefore, the factoring of a² - 121 would be:

(a - 11)(a + 11)

Among the given options A) (a - 11)(a + 11), B) (a - 121)(a + 1), C) (a - 11)(a - 11), and D) (a + 11)(a + 11), option A is correct because it correctly represents the factored form of a difference of squares.