Assignments: 12-Combining Like Terms
Combining Like Terms is a process used to simplify an expression or an equation using addition and subtraction of the coefficients of terms. Consider the expression 5 + 7. By adding 5 and 7, you can easily find that the expression is equivalent to 12
The key to understanding Combining Like Terms is the meaning of the phrase like terms and being able to identify them. Here are a few examples of like terms:
***The following terms are like because they have just one variable, x, with a coefficient:
2x, 45x, x, -26x, -2x
***The following terms are like because they are all just simple numbers:
15, -2, 27, 2046, 0.6
***The following terms are like because they are y² with a coefficient:
3y², y², -y², 26y²
Please note that terms with exponents are not like terms without, so 5x² is not a like term to 3x.
Algebraic expressions can also be simplified by combining like terms. consider the equation
12x + 7 + 5x
Because 12x and 5x have the same single variable with only a coefficient, they are like terms and can be added together. 12+5=17 so 12x+5x=17x. The expression would be simplified to
17x+7
Here is a more complex example:
5x² + 7x + 2 – 2x² + 7 + x
The commutative property tells us we can rearrange the addition without consequence. This can help us to put like terms together.
(5x² - 2x²) + (7x + x) + (2 + 7)
We can then simplify it by doing the basic operations between the like terms.
3x² + 8x + 9