factor 16x^2-121
(4x - 11)(4x + 11)
To factorize the quadratic expression 16x^2 - 121, we need to find two binomial factors whose product will give us the original expression.
Step 1: Identify the expression as a difference of squares
Since we have a perfect square term (16x^2) subtracted from another perfect square term (121), we can recognize this as a difference of squares. The difference of squares formula is a^2 - b^2 = (a + b)(a - b).
Step 2: Apply the difference of squares formula
In this case, a^2 is 121 and b^2 is 16x^2.
(121 - 16x^2) can be written as (11)^2 - (4x)^2, which follows the difference of squares form.
Step 3: Factorize using the difference of squares formula
Applying the formula, we have:
16x^2 - 121 = (11 + 4x)(11 - 4x)
So, the factorization of the quadratic expression 16x^2 - 121 is (11 + 4x)(11 - 4x).