Question

Factor the difference of two squares. 16x^2-49. Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.

A.16x^2-49=?
B. The polynomial is prime.

Answer 1

The expression 16x^2-49 is a difference of squares and can be factored into (4x + 7)(4x - 7) following the formula a^2 - b^2 = (a + b)(a - b).

Step-by-step explanation:

The given expression, 16x^2 - 49, is a difference of two squares. We can use the formula a^2 - b^2 = (a + b)(a - b) to factor it.

Here, a = 4x and b = 7. Plugging these values into the formula, we get:

16x^2 - 49 = (4x + 7)(4x - 7)

So, the factored form of the expression is (4x + 7)(4x - 7).

The difference of two squares is a specific type of polynomial that can be factored into the product of the sum and difference of two terms. In this case, the expression 16x^2-49 represents a difference of squares because both 16x^2 and 49 are perfect squares. The factorization would split the expression into two binomials: (4x)^2 - (7)^2. Following the difference of squares formula, which is a^2 - b^2 = (a + b)(a - b), we obtain the factors (4x + 7)(4x - 7).

Therefore, the correct choice is A, and the factorization of the polynomial 16x^2-49 is (4x + 7)(4x - 7).