Question

Factor the perfect squares. $$ x^{2}-4 x+4 $$

   Factor the perfect squares.
$$
x^{2}-4 x+4
$$

College Algebra

College Algebra

Michael Sullivan 10th Edition

Chapter 0, Problem 28

Instant Answer

Solved by Expert Patrick Burns

05/08/2020

Step 1

The general form is $a^2 \pm 2ab + b^2$. In our case, we have $x^2 - 4x + 4$. Show more…

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Factor the perfect squares. $$ x^{2}-4 x+4 $$

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Key Concepts

Perfect Square Trinomials

A perfect square trinomial is a quadratic expression that results from squaring a binomial. The general form is a^2 ± 2ab + b^2, which can be factored into (a ± b)^2. Recognizing this pattern helps simplify the factoring process significantly.

Factoring Quadratic Expressions

Factoring quadratic expressions involves rewriting a quadratic polynomial as a product of two binomials. By identifying special patterns, such as perfect square trinomials, one can quickly factor and simplify the expression, making solving equations and further algebraic manipulation easier.

Polynomial Identities

Polynomial identities, such as (a ± b)^2 = a^2 ± 2ab + b^2, form the basis for understanding and factoring various types of polynomial expressions. These identities are useful tools in algebra for both expanding binomials and recognizing factorable patterns within more complex expressions.

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