Combine Like Terms Notes Page 23

Combining Like Terms Now that we have seen some algebraic expressions, we need to know how to simplify them. Vocabulary Like terms: In an expression, like terms are the terms that have the same variables, raised to the same powers (same exponents). i.e. 4x and -3x or 2y2 and –y2 Coefficient: A constant that multiplies a variable. i.e. the 3 in 3a or the -1 in –b

Combining Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms. Like terms include letters that are the same and numbers.

Let’s try one… Step One: Write the expression. 4x + 5x -2 - 2x + 7 Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. 4x, 5x, and -2x -2 and 7 Simplify the variable terms. 4x+5x-2x = 9x-2x = 7x Simplify the constant (number) terms. -2+7 = 5 You have a simplified expression by writing all of the results from simplifying. 7x + 5

Another example… 10x – 4y + 3x2 + 2x – 2y 3x2 10x, 2x -4y – 2y Remember you cannot combine terms with the same variable but different exponents.

Now you try… Simplify the following: 5x + 3y - 6x + 4y + 3z 3b - 3a - 5c + 4b 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 5xy – 2yx + 7y + 3x – 4xy + 2x A A A A

You Try #1 Simplify the following: 5x + 3y - 6x + 4y + 3z 5x, -6x 3y, 4y 3z -x + 7y + 3z

You Try #2 Simplify the following: 3b - 3a - 5c + 4b 3b, 4b -3a -5c -3a + 7b – 5c

You Try #3 Simplify the following: 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 4ab, -ab -2a2b, 2a2b 5, 4 ab2 3ab + ab2 + 9

You Try #4 Simplify the following: 5xy – 2yx + 7y + 3x – 4xy + 2x 5xy, -2yx, -4xy 7y 3x, 2x -xy + 7y + 5x