Algebraic Pattern Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
What pattern does 9x2−169x^2 - 16 match?

Solution

  1. 1
    (3x)2−42(3x)^2 - 4^2: difference of squares.
  2. 2
    (3x+4)(3x−4)(3x + 4)(3x - 4).

Answer

Difference of squares: (3x+4)(3x−4)(3x + 4)(3x - 4)
Training yourself to see 9x29x^2 as (3x)2(3x)^2 and 1616 as 424^2 is the key skill. Pattern recognition turns a factoring problem into a direct application of a known formula.

About Algebraic Pattern

A recognizable, recurring algebraic structure such as a2−b2a^2 - b^2 or (a+b)2(a+b)^2 that can be applied systematically.

Learn more about Algebraic Pattern →

More Algebraic Pattern Examples

Example 1 easy

Identify the pattern and factor: [formula].

Example 2 hard

Factor [formula] by identifying the pattern.

Example 4 medium

Simplify [formula].

← All Algebraic Pattern Examples Algebraic Pattern Concept