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When simplifying algebraic expressions, a key step is to combine like terms. This means you group together terms that have the same variable.

Suppose we have the expression \begin{array}{c} -22 p+17 q+(-35 p)+(-27 q) oindent We can simplify it by combining the terms with the same variables. First, let's look at the terms with the variable \(p\): \(-22p\) and \(-35p\). Add these two terms together by their coefficients: \(-22 + (-35) = -57\).

This gives us \(-57p\).

Next, combine the terms with the variable \(q\): \(+17q\) and \(-27q\). Add these terms together as well: \(17 + (-27) = -10\).

Now we have \(-10q\).

After combining like terms, the simplified expression is \(-57p - 10q\).

Paddling down and organizing the like terms makes algebra more manageable and keeps everything clear!

Variables are symbols used to represent numbers in algebraic expressions and equations. They allow us to write general statements and solve problems more flexibly.

In our example, the variables are \(p\) and \(q\). Each variable stands in for an unknown or variable quantity. When simplifying expressions involving variables, we treat each variable as a separate entity.

The coefficient of a variable is the number multiplying the variable, such as \(-22\) in \(-22p\).

When combining like terms, only the coefficients are added or subtracted, not the variables themselves. Understanding this concept helps you manipulate and make sense of algebraic expressions more effectively.

Always remember, variables in algebra denote quantities that can change, giving us powerful tools to express and solve real-world problems.

Basic algebra serves as the foundation for higher-level math problems and various real-world applications. It involves operations and principles that help simplify and solve equations.

Key components of basic algebra include:

• Combining like terms: Grouping terms with the same variable to simplify expressions.
• Constants: Numbers without variables that stand alone, e.g., +2 or -5.
• Variables: Symbols like \(p\) and \(q\) used to represent unknown quantities.
• Coefficients: Numbers that multiply variables, such as 3 in 3x.

A good grasp of basic algebra makes complex problems more approachable. Once you're comfortable with simplifying expressions and combining like terms, you'll find it easier to progress to more advanced topics and algebraic equations.