Add or subtract terms whenever possible. $4\sqrt{13x} - 6\sqrt{13x}$

Verified step by step guidance

1. Identify the like terms in the expression. Both terms have the radical \( \sqrt{13x} \), so they are like terms and can be combined.
2. Rewrite the expression to clearly show the coefficients and the radical: \( 4\sqrt{13x} - 6\sqrt{13x} \).
3. Combine the coefficients of the like terms by subtracting: \( 4 - 6 = -2 \).
4. Multiply the result by the common radical term: \( -2 \times \sqrt{13x} \).
5. Write the simplified expression as \( -2\sqrt{13x} \).

Key Concepts

Like Terms

Like terms are terms that have the same variable parts raised to the same powers. In this problem, terms involving √13x are like terms because they share the same radical expression. Only like terms can be added or subtracted by combining their coefficients.

Simplifying Radicals

Simplifying radicals involves expressing the radical in its simplest form by factoring out perfect squares. Here, √13x is already simplified, so no further simplification is needed before combining terms. Recognizing simplified radicals helps in correctly identifying like terms.

Combining Like Terms

Combining like terms means adding or subtracting their coefficients while keeping the variable or radical part unchanged. For example, 4√13x − 6√13x equals (4 − 6)√13x = −2√13x. This process simplifies expressions and is essential for solving algebraic problems efficiently.