Factor each polynomial. See Examples 5 and 6. (a+b)^2-16

Factoring polynomials involves rewriting a polynomial as a product of its simpler components, or factors. This process is essential for simplifying expressions and solving equations. Common techniques include identifying common factors, using special product formulas, and applying methods like grouping or the quadratic formula.

The difference of squares is a specific factoring pattern that applies to expressions of the form a^2 - b^2, which can be factored into (a - b)(a + b). In the given polynomial (a + b)^2 - 16, recognizing it as a difference of squares allows for efficient factoring, as 16 can be expressed as 4^2.

Special product formulas are algebraic identities that simplify the multiplication of binomials. For example, (a + b)^2 = a^2 + 2ab + b^2 is a key identity. Understanding these formulas helps in recognizing patterns in polynomials, making it easier to factor expressions like (a + b)^2 - 16 by first expanding or simplifying them.