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In algebra, combining like terms is an essential skill that helps simplify expressions. To do this, you need to identify terms in an expression that have the same variable raised to the same power. For instance, in the expression \(3x + 2x\), \(x\) is the common variable both terms have.- **Identify Like Terms**: Terms such as \(3x\) and \(2x\) are like terms because they share the variable \(x\) raised to the same power. - **Add or Subtract Coefficients**: Once you identify like terms, add or subtract their coefficients. For \(3x + 2x\), you add 3 and 2, which results in \(5x\). This is how you combine like terms.Knowing how to combine like terms simplifies your expressions and makes them easier to solve. Keep practicing, and you'll find that this becomes a quick step in manipulating algebraic expressions.

Distributing negative signs is a process used when you have a subtraction, or negative sign, in front of a group of terms. This is crucial in making sure each term in the group changes its sign correctly.Let's break it down:- **Identify the Negative Sign**: Look for a negative sign before parentheses, such as in \( -(8 - 2x) \). - **Distribute to Each Term**: Apply the negative sign to each term inside the parentheses. If you have \(-(8 - 2x)\), it becomes \(-8 + 2x\). This changes the signs within the group. The positive 8 becomes negative, and the negative 2x becomes positive 2x.This technique ensures that every term within the parentheses receives the negative sign, preventing any mistakes in your calculations later on.

Simplifying expressions makes them neater and easier to understand or solve. It combines several strategies which all work together:- **Combine Like Terms**: As seen earlier, this involves grouping terms with the same variables and consolidating their coefficients. - **Distribute Signs**: Before simplifying, make sure you correctly distribute any negative signs across terms as necessary.Once you have combined like terms and distributed any negative signs, your expression should be much simpler. Consider an example: From \(3x^2 + x - 8 + 2x\), you combine \(x\) and \(2x\) to yield \(3x\), resulting in \(3x^2 + 3x - 8\). Now, the expression is simplified and easier to interpret or further solve.