Combine Like Terms 10x+5y-6x-2y

Solution:

Step 1:

Combine the terms with $x$ by subtracting $6x$ from $10x$. The result is $4x+5y-2y$.

Step 2:

Now, combine the terms with $y$ by subtracting $2y$ from $5y$. The simplified expression is $4x+3y$.

Knowledge Notes:

Combining like terms is a fundamental process in algebra which involves simplifying algebraic expressions by adding or subtracting terms that have the same variable raised to the same power. Here are the relevant knowledge points for this problem:

1. Like Terms: Terms that have the same variable(s) with the same exponent(s) are called like terms. For example, $2x$ and $5x$ are like terms because they both contain the variable $x$ raised to the first power.

2. Combining Like Terms: To combine like terms, you add or subtract the coefficients (the numerical parts) and keep the variable part unchanged. For instance, $2x+3x=(2+3)x=5x$.

3. Simplifying Expressions: The process of combining like terms is part of simplifying expressions. Simplifying makes expressions easier to work with by reducing them to their simplest form.

4. Subtraction of Terms: When subtracting terms, you subtract the coefficients and keep the variable part the same, just as with addition. For example, $10x-6x=(10-6)x=4x$.

5. Coefficients: These are the numbers in front of the variables. In the term $5y$, $5$ is the coefficient.

6. Constants: Terms without variables are called constants and are combined separately from variable terms.

7. Order of Operations: While combining like terms, the order of operations (PEMDAS/BODMAS) doesn't usually affect the process since you are only dealing with addition and subtraction of like terms.

In the given problem, the expression $10x+5y-6x-2y$ contains two pairs of like terms. The terms $10x$ and $-6x$ are like terms, as are $5y$ and $-2y$. By combining these like terms, the expression is simplified to $4x+3y$.