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## Collecting Like Terms

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**Collecting Like Terms**orms ?**A term in math is a piece of an expression separated by a**plus or minus sign. In the expression 3x + 4y – 7 There are three terms.**We know what a term is now, so what are like terms?**Like terms are terms that have identical variable pieces. In other words, the letters match.**x, y, and z are all different variables. So each of these**is a different term. x and x are the same, so they are called like terms. z and z would also be like terms.**Let’s forget about math for a few minutes.**Instead of talking about terms let’s talk about worms. “Why worms?” You ask. Because they’re so cute.**We have two types of worms. Let’s collect the worms into**groups by color.**Back to math. Instead of worms, now we have terms. Instead**of grouping by colors we group by the same variables. (like terms) x y x y x**Just imagine the letters are worms and collect them like**before. x y x x y**Now count up how many of each we have.**x y x 3 x y 2**Let’s look at this as an expression.**Just as before, count up how many of each term you have. x + x + y + x + y 3 x’s and 2 y’s We write this as 3x + 2y**But worms are social creatures. Well, not really, but what**if they’re traveling in groups instead of individually?**In this case we take the number in each group and combine**them. 4 3 3**Now combine like worms, brown with brown, and yellow with**yellow. Since there is only one group of yellow it does not combine with any other worms. 4 7 3 3 The expression is now: 7 3**Let’s look at some examples.**• 3x + 4y + 2x • 7x + 2y + 6x + 3y • 12z + 14z + 13z = 5x + 4y = 13x + 5y = 39z**Collecting like terms(worms) can also be used when reducing**a group. We can subtract or add negative amounts. For example, on the expression 4x + 3y + 2x we add the like terms to get 6x + 3y. However, on the expression 4x + 3y – 2x we subtract the x’s to get 2x +3y.**The trick to subtraction is to remember that each number**goes with the sign or operation that comes before it. 4x + 7y – 3x – 2y + 3z – 2y Now collect like terms: x + 3y + 3z**Try these.**= 2x + 3y • 4x + 3y -2x • 7x – 6y – 4x + 8y • 7z + 8x – 3z – 10x = 3x +2y =-2x +4z When we end up with a negative amount we can write a minus sign instead of a plus sign with a negative number.**What about exponents?**X2 is like X∙X These are connected by multiplication and not addition or subtraction. This means that X2 is a single term. Here are some other examples of terms with multiple variables: X3, Y5, XY, XZ, XYZ, X2Y, X5Y3Z4**Try these examples.**• 3x2 + 7xy + 5x2 + 3xy • 4x2 + 5x + 2x3 + 8x2 + 2x • 5xy + 3x + 4yx + 4y = 8x2 + 10xy Remember x, x2, and x3 are different terms. You only combine like terms. = 2x3 + 12x2 + 7x By the commutative property we can rearrange multiplication, so xy = yx, these are like terms. = 9xy +3x +4y**Still having trouble?**• Try color coding, use colored pencils to identify the like terms. • Or use pictures for the situation (like worms). + 4xy + 6x + 2xy 4y 3x + + + + 6x 2xy 4y 3x + 4xy