91Ó°ÊÓ

When combining like terms, it's essential to identify terms that have the same variable part. In the exercise, we had the terms \(6r\) and \(8r\). Both terms contain the variable 'r'.

Like terms are terms that have the same variable raised to the same power. They can be combined by adding or subtracting their coefficients. For instance, in the case of \(6r + 8r\), both terms have 'r', which makes them like terms.

By recognizing like terms, we simplify expressions and solve equations more easily. Always look for terms with the same variables before combining them.

Coefficients are the numerical part of a term that is multiplied by the variable. In the exercise, the coefficients are 6 and 8 in \(6r\) and \(8r\) respectively.

When combining like terms, you add or subtract the coefficients while keeping the variable part unchanged. So, when we see \(6r + 8r\), we add 6 and 8 to get 14.

Another way to think about coefficients is that they are the 'scaling factor' of the variable. In \(6r\), 6 tells us how many times 'r' is being summed.

Understanding coefficients helps us manipulate and simplify algebraic expressions correctly. They are key to accurately combining like terms.

Variables are symbols used to represent unknown numbers or quantities in mathematical expressions and equations. In the exercise, the variable is 'r'.

Variables can be any letter, but commonly used ones are x, y, and z. In terms like \(6r\) and \(8r\), 'r' is the variable. The power of the variable also plays a role in identifying like terms.

If you had terms like \(6r\) and \(8r^2\), they wouldn't be like terms because the powers of 'r' are different. Combining like terms requires the variable and its power to be the same in all terms.

Variables allow us to create general formulas and equations that can solve a wide array of problems. They are the foundation of algebra, making it possible to perform systematic manipulations.