what is the like term method ?
The like term method is a technique used in algebra to simplify expressions or combine terms that have the same variables raised to the same powers. It involves identifying terms with the same variables and exponents and then combining them using addition or subtraction.
To apply the like term method, you'll need to follow these steps:
1. Identify like terms: Look for terms that have the same variable(s) raised to the same power(s). For example, in the expression 3x^2 + 5x^2 - 2xy + 4xy, the terms 3x^2 and 5x^2 are like terms because they have the same variable (x) raised to the same power (2). Similarly, -2xy and 4xy are also like terms because they have the same variables (x, y), even though the exponents are 1.
2. Combine the coefficients: Once you have identified the like terms, add or subtract their coefficients. The coefficients are the numbers that multiply each term. In the example above, 3x^2 + 5x^2 = 8x^2, and -2xy + 4xy = 2xy.
3. Keep the variable(s) and exponent(s): After combining the coefficients, write down the variable(s) and exponent(s) exactly as they appear in the like terms. In our example, we keep the x^2 and xy terms unchanged.
4. Combine any remaining terms: If there are any non-like terms remaining, keep them as they are. In the example, -2xy + 4xy already combined to 2xy, so the only remaining term is 8x^2.
Therefore, the simplified expression using the like term method is 8x^2 + 2xy.