Factor each polynomial. See Examples 5 and 6. 9a^2-16

Key Concepts

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its simpler components, or factors. This process is essential for simplifying expressions, solving equations, and understanding the polynomial's roots. Common methods include factoring out the greatest common factor, using special products, and applying techniques like grouping.

Difference of Squares

The difference of squares is a specific factoring pattern that applies to expressions in the form a^2 - b^2, which can be factored as (a - b)(a + b). In the given polynomial 9a^2 - 16, both 9a^2 and 16 are perfect squares, making this pattern applicable. Recognizing this pattern is crucial for efficient factoring.

Perfect Squares

Perfect squares are numbers that can be expressed as the square of an integer or a variable. In the context of polynomials, terms like 9a^2 (which is (3a)^2) and 16 (which is 4^2) are perfect squares. Identifying perfect squares is vital for applying the difference of squares method effectively in polynomial factoring.