Algebraic Pattern Math Example 1

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

easy

Identify the pattern and factor:

x^2 - 2x + 1

1
Step 1: Recognize: $x^2 - 2(x)(1) + 1^2$ matches $(a-b)^2 = a^2 - 2ab + b^2$ .
2
Step 2: $a = x, b = 1$ , so $(x - 1)^2$ .
3
Check: $(x-1)^2 = x^2 - 2x + 1$ ✓

Answer

(x - 1)^2

Pattern recognition speeds up algebra enormously. Recognizing

a^2 \pm 2ab + b^2

as a perfect square trinomial is faster than the sum-product method.

About Algebraic Pattern

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

Factor [formula] by identifying the pattern.

What pattern does [formula] match?

Simplify [formula].