Combining Like Terms

Combining Like Terms Is this a “positive 5” or “plus 5”? +5 BOTH

Combining Like Terms HINT: If you don’t see a negative or positive sign in front of a number it is always positive. 5 +

Combining Like Terms Is this a “negative 7” or “minus 7”? -7 BOTH

–7 HINT: The sign in front of the number BELONGS TO THE NUMBER! Combining Like Terms HINT: The sign in front of the number BELONGS TO THE NUMBER! –7

Combining Like Terms “Simplify” means to combine like terms and complete all operations 2x + 2x + 3x = 7x

You can combine terms that are alike. Combining Like Terms Terms in an expression are like terms if they have identical variable parts. You can combine terms that are alike.

To look at combining like terms we are going to use ALGEBRA TILES! Algebra Tiles help us to visualize what each term represents.

Algebra Tiles Combining Like Terms Area = x Area = 1 Area = x2 Large Square Rectangle Small Square 1 x x 1 Area = 1 1 x Area = x Area = x2

I have 5x + 4 Algebra Tiles How much do I have here? Combining Like Terms Algebra Tiles How much do I have here? I have 5x + 4

Algebra Tiles I have x2 + 2x + 6 How much do I have here? Combining Like Terms Algebra Tiles How much do I have here? I have x2 + 2x + 6 Notice that we write the largest shape first, then the medium size, then the smallest. We write them in order from largest to smallest.

Algebra Tiles Combining Like Terms 6 x2 x x x2 x You can only combine terms that are alike, or terms that have the same variable. 6 x2 x x x2 x When I combine like terms I have 2x2+ 3x + 6

Combining Like Terms Algebra Tiles You are going to get your own set of algebra tiles to use. Take them out of the bag and put them on your desk. The red should be on the bottom.

Algebra Tiles Combining Like Terms Area = x Area = 1 Area = x2 Large Square Rectangle Small Square 1 x x 1 Area = 1 1 x Area = x Area = x2

Algebra Tiles Combining Like Terms Area = -x Area = -1 Area = -x2 Large Square Rectangle Small Square 1 x x -1 Area = -1 -1 -x Area = -x Area = -x2

Show me 3 + x2 with your tiles Combining Like Terms Algebra Tiles Show me 3 + x2 with your tiles Since no terms are alike, we can’t combine anything, so my answer is x2 + 3

Show me x +3 + 2x with your tiles Combining Like Terms Algebra Tiles Show me x +3 + 2x with your tiles We can combine the terms that are alike. So my answer is is 3x + 3

Algebra Tiles Show me 3x + 2 + x + 4 with your tiles Combining Like Terms Algebra Tiles Show me 3x + 2 + x + 4 with your tiles We can combine the terms that are alike. So my answer is is 4x + 6

= 6x + 5 = 3x2+ 2x + 4 = 4x2 +3x+2 Combining Like Terms Try these problems with your algebra tiles. Combine like terms. Give me a thumbs up when you know the answer. = 6x + 5 2x + 4 + 4x + 1 2x2 +2x + 3 + x2 + 1 1 + 3x + 3x2 + 1 + x2 = 3x2+ 2x + 4 = 4x2 +3x+2

Like terms can be combined! Like Terms Unlike Terms Combining Like Terms Like terms can be combined! Like Terms Unlike Terms

Combine the following like terms. Combining Like Terms Combine the following like terms. 1) 3x + 5y + 4x Say these! 7x + 5y 2) 4a + 6 - 3a - 2 a + 4

Combine the following like terms. Combining Like Terms Combine the following like terms. Say these! 3) x + 3y + 2x + 4y - z 3x + 7y - z 4)

Combining Like Terms 1) 7m - 2m + 8m 4) -3k + 5k + -k + 2k Say these! 2) -3y + y - 8y 5) t - 4t + -3t + 2t -10y -4t 3) 11r - 5r - 9r 6) 11x - 4x + x + -3x -3r 5x

Take Out Your Study Guide!!! Combining Like Terms Put your algebra tiles back in your bag and ziplock them. Pass your tiles forward quickly. That's all Folks! Take Out Your Study Guide!!!

#5 Terms Terms are in expressions or equations, and they are separated by addition or subtraction signs. 3 terms 6x2 + 3x - 4 6 x2 x x x x2 When I combine like terms I have 2x2+ 3x +6 Write terms in order from largest shape to smallest.

#6 Combine Like Terms 1) 7x - 4y + 2x - y 1 You can only combine terms that are alike, or terms that have the same variable. 9x - 5y 2) 3m + 10n - 4m + 1 -m + 10n + 1 3) 6a - (5a) + 2a + (-3) 3a - 3 4) 4k - (2j) - 6k - j -2k - 3j

Extra slides

xy x2 y2 x x x x y y y y #Extra Algebra Tiles A = x • x A = 1 • x A = x • y y y y y2 1 1 -1 1 1 -1 y 1 A = 1 A = -1 A = y • y = y2 A = 1 • y = y