COMBINING LIKE TERMS People who are identical twins

COMBINING LIKE TERMS

People who are identical twins are a “like pair” because they have the exact same features. An Algebraic Equation we can write for this is: t + t = 2 t One Twin + One Twin = 2 Twins. In Algebra we call this: “Combining Like Terms”.

terms- parts of an expression separated by an addition (+) or subtraction (-) sign. Example: 34 g + 18 – 3 p + 4 s This expression has ____ terms 4 like terms- terms that contain the same variable/same EXACT groups of variables. Example: 2 b + 3 b 2 b and 3 b are LIKE terms because they both have the variable “b” in them Please Note: 2 ab and 3 b are not like terms, because one has an a in it.

Consider these two expressions: 8 x + 7 xy LIKE TERMS UNLIKE TERMS

Decide if the terms in each pair of items are “Like Terms” or “Unlike” Unlike (don’t have the same variable) 1) 4 g and 4 h ______ Like (have the same variable) 2) 3 h and 5 h ______ Unlike (don’t have the same exact variables) 3) 5 x and 4 xy ______ Like (have the same exact variables) 4) 8 rp and 7 rp ______ Unlike (don’t have the same variable) 5) 4 g and 4 y_______ Like (have the same variable) 6) 2 c and 20 c______ Like (have the same variable) 7) y and 6 y______ Like (have the same variables) 8) 2 ab and 6 ba ______

A typical algebraic expression is : 2 a + 3 b + 3 a +4 b We can think of “a” as being Apples and “b” as being Bananas, That expression can be represented as: We can combine the like objects. The above can be simplified to be 5 Apples and 7 Bananas. Which in Algebra is: 5 a + 7 b 2 a + 3 b + 3 a + 4 b = 5 a + 7 b

Often in real life, it is necessary to combine like items together to create a shorter list of items we can deal with. For example, a family orders food from Burger King. Here is the order: Using Algebra we could write it as: 2 b + 1 f + 1 d + 3 b + 2 f + 2 d If we combine like items, we get a simplified list as follows: 5 b + 3 f + 3 d

When combining like terms we combine everything that is the same: 3 x + 4 x + 8 y - 7 x 3 y So our solution is: 7 x + 3 y 5 y

Here is an expression containing 4 terms with two sets of LIKE terms: 6 y 3 x + 4 y + 2 x + 2 y 5 x 5 x + 6 y

Practice 11 e 6 b + 3 e + 7 b + 8 e 13 b + 11 e

Practice 9 y 13 z + 3 y + 9 + 6 y + 7 z 20 z + 9 y + 9

We can Subtract Like Terms Also. Suppose that we have bought 5 apples and 6 bananas, But we eat two bananas before putting our fruit into the bowl. The Algebra is: 5 a + 6 b – 2 b (6 bananas take away 2 is 4) 5 a + 4 b