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In algebra, coefficients are the numbers that are placed in front of variables in an expression. They play a crucial role in determining the value and magnitude of a term. For example, in the term \(7x\), the number 7 is the coefficient. This tells us how many times the variable \(x\) is being multiplied. By understanding coefficients, we can easily manipulate and simplify mathematical expressions.

When working with expressions, always identify the coefficients of each term. These are the numbers you adjust when combining like terms. Consider coefficients like labels that help us keep track of how much of each variable we have. When terms share the same variable, we add or subtract their coefficients to combine them. This simplifies expressions and makes them easier to work with.

Like terms are terms in an expression that have the exact same variable factor. In simple terms, the variables in these terms need to be identical for them to be combined. For example, in the expression \(7x + 9x\), both terms have the variable \(x\), which makes them like terms. The idea is that only like terms can be combined through addition or subtraction.

To identify like terms, look for:

• Similar variables.
• The same exponent for each variable.

If two terms have the same variable with the same power, they can be combined by adding or subtracting their coefficients. This understanding allows us to reduce expressions to a simpler form, making them far easier to work with and solve.

Simplifying expressions is the process of reducing complex algebraic expressions to their simplest form. The goal is to make the expression more straightforward and less cluttered by performing operations like combining like terms.

Here's how you simplify expressions:

• Identify like terms, which are terms with the same variable and exponent.
• Combine these like terms by adding or subtracting their coefficients.
• Rewrite the expression with the new coefficients applied to the respective variables.

In the exercise, we simplified \(7x + 9x\) to \(16x\) by adding the coefficients 7 and 9. That's all it takes to simplify expressions: Identify, combine, and rewrite. Keeping an expression simplified not only saves time in solving but also reduces the possibility of making errors.