To add like terms, find the terms that have the same (or no) variable, and combine the coefficients of the terms. For instance, if you have a+b where a and b are real numbers, you can combine them.
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Terms with the same variable(s). In like terms, you may add, subtract, multiply, or divide them. In the equation 3x - 5ax + 9x = 7ax, the 5x and the 10x are like terms because they both contain variables of the same value. Thus, we are allowed to add them up and get 12x. The -5ax and the 7ax are also like terms and if we add 5ax to both sides (after we add 3x to 9x), we'll get the equation 12x = 12ax.
When combining like terms, you could add and multiply. It depends on what the problem is. I am in 6th grade and currently learning algebra. I know that my answer is correct because I already learned this.
Terms like 2x and 4x2 are not like terms. In order for terms to be like terms, they must have the exact same variables with the exact same exponents on them. This means that 5x3 and 7x3 are like terms, but 2x and 4x2 are not. To add or subtract like terms, simply add or subtract the coefficients (the numbers in front) and keep the variable part the same. For example, 5x3 + 7x3 = (5 + 7)x3 = 12x3, and 3x2 + 6x2 = (3 + 6)x2 = 9x2. But, since 2x and 4x2 are not like terms, 2x + 4x2 = 2x + 4x2. It just cannot be simplified any more than that.
When combining like terms like 2x+3x we add their coeffitients, for example 2x+3x=(2+3)x=5x
4v-7+8v+4-5 - add the like terms =12v-8 12v and 8 cannot be subtracted because they are not like terms. Like terms have the same variable.