Factorization using the Difference of Two Squares

An expression of the form ( a^2 - b^2 ) can be written as ( (a + b)(a – b) ).

1. Factorize: ( x^2 - 16 )

Step 1: Recognize the expression as a difference of two squares.
x^2 - 16 = x^2 - 4^2

Step 2: Apply the formula (a^2 – b^2 = (a – b)(a + b)):
(x - 4)(x + 4)

Final Answer:
\boxed{(x - 4)(x + 4)}

2. Factorize: ( 9y^2 - 25 )

Step 1: Write each term as a square.
9y^2 = (3y)^2 \quad \text{and} \quad 25 = 5^2

Step 2: Apply the difference of two squares formula:
(3y - 5)(3y + 5)

Final Answer:
\boxed{(3y - 5)(3y + 5)}

3. Factorize: ( 4a^2 - 49b^2 )

Step 1: Express both terms as perfect squares.
4a^2 = (2a)^2 \quad \text{and} \quad 49b^2 = (7b)^2

Step 2: Apply the difference of two squares formula:
(2a - 7b)(2a + 7b)

Final Answer:
\boxed{(2a - 7b)(2a + 7b)}