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In algebra, when working with expressions, the term 'like terms' frequently comes up. Like terms are components of an algebraic expression that have the same variable factors raised to the same powers. For example, in the expression \(-16 a^{4} b^{2}+10 a^{4} b^{2}\), both terms are considered like terms because they involve the same exact variables: \(a^{4} b^{2}\).
Identifying like terms is a key step in simplifying algebraic expressions. Once like terms are identified, they can be combined into a single term, which makes the expression easier to work with or solve.

• The coefficients are the numbers in front of the variables, like -16 and 10 in our case.
• Only the coefficients can differ among like terms, but the variable part must be identical.

Recognizing like terms allows for simplification by merging them into fewer terms without changing their overall value in the expression.

An algebraic expression is a mathematical phrase combining numbers, variables, and operation symbols. It doesn't have an "equals" sign, which distinguishes it from an equation. Algebraic expressions represent real-world quantities in many scenarios and are foundational in algebra studies.
The expression \(-16 a^{4} b^{2}+10 a^{4} b^{2}\) contains two terms separated by a plus sign. Each term is made up of:

• A coefficient, which is the numeric part (e.g., -16 and 10).
• A variable part, which, in this case, includes \(a^{4}\) and \(b^{2}\).

To simplify an algebraic expression, focus on combining like terms and clearing up any unnecessary operations. This is done by aligning terms with identical variables to streamline the overall expression.

Combining terms involves adding or subtracting their coefficients while keeping the variable part intact. This concept typically applies when you have identified like terms within an algebraic expression.
For the expression \(-16 a^{4} b^{2}+10 a^{4} b^{2}\), combining terms is straightforward:

• Keep the common variable part \(a^{4} b^{2}\).
• Add the coefficients of the like terms: \(-16 + 10\).
• This results in a simplified coefficient of \(-6\), giving us the expression \(-6 a^{4} b^{2}\).

Once like terms are combined, the expression is shorter and easier to understand or further manipulate. Combining terms reduces complexity and clarifies the components of larger algebraic expressions.