In Exercises 21–32, simplify by factoring. ___ √40x

Key Concepts

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In algebra, this often involves identifying common factors or applying special product formulas, such as the difference of squares or perfect square trinomials. Understanding how to factor is essential for simplifying expressions and solving equations.

Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 40 can be expressed as √(4 × 10), which simplifies to 2√10. Recognizing how to simplify square roots is crucial in algebra, especially when dealing with expressions that involve radical signs.

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, etc. Simplifying radical expressions often requires factoring the radicand (the number under the root) into its prime factors and identifying perfect squares or cubes. Mastery of radical expressions is important for performing operations like addition, subtraction, and multiplication involving roots.