91Ó°ÊÓ

Understanding like terms is essential when adding or subtracting monomials. Like terms have the same variable part raised to the same power. In the exercise \[6x^2 + 9x^2\], both terms are like terms because they both have the variable part \[x^2\]. This similarity allows us to add or subtract them simply by focusing on their coefficients.
For instance, \(3x\) and \(5x\) are like terms because they both have the variable \(x\).
However, \(4x^2\) and \(4x\) are not like terms because the variable parts are different; one is \(x^2\) and the other is \(x\).
Always check the variable part to determine whether the terms are like terms.
If they are not like terms, you cannot combine them directly using addition or subtraction.

The coefficient is the numerical part of a term and is found in front of the variable part. In the expression \[6x^2 + 9x^2\], the coefficients are 6 and 9.
When adding or subtracting monomials, you only work with the coefficients, provided that the terms are like terms.
In our example, the solution adds the coefficients: \[6 + 9 = 15\] and keeps the variable part unchanged, leading to the result \[15x^2\].
Here's another example: \[4x - 3x = (4-3)x = 1x = x\].
In this case, the coefficients 4 and -3 are subtracted to give 1, and the variable part \(x\) remains the same.
If you have different variable parts, you cannot combine the coefficients in this manner.

The variable part of a monomial includes the variable itself and any exponents attached to it. For instance, in the monomial \[6x^2\], the variable part is \[x^2\]. This means the variable is \(x\) raised to the power of 2.
It is important to note that for two monomials to be considered like terms, their variable parts must be identical.
This includes both the variable and the exponent.
This is why \(6x^2\) and \(9x^2\) are like terms, but \(4x\) and \(5x^2\) are not, even though they both involve the same variable \(x\).
Understanding the variable part helps in identifying like terms accurately and working correctly with their coefficients.