Page 12-17 Mr. Peter Richard’s Awesome Class! 1.5 Combining Like Terms Page 12-17 Mr. Peter Richard’s Awesome Class!

Simplify Expression Simplify: Combine like terms 3 dogs + 3 cats + 5 dogs = 3d + 5c + 6d = Like terms- because they both have d as a variable (Just add the coefficients # with the variable) 8 dogs + 3 cats 9d + 5c

Terms must match in variable and exponent EXAMPLES x 2x 3x -x -2x -3x y 2y 3y -y -2y -3y X2 2x2 3x2 -x2 -2x2 -3x2 y2 2y2 3y2 -y2 -2y2 -3y2 1 2 3 -1 -2 -3

Simplify Each Expression 3x + 2x = 5x 8y – 2y + 5 = 6y + 5 8y – 2y = 6y 4k + 17 - 2k = 2k + 17 4k – 2k = 2k Watch the sign in front of the number!!!!

Simplify Each Expression 2b – 8 + 4b – 6b -19 – 11a + a + 16 1 2b + 4b – 6b = 0b -19 + 16 = - 3 -8 -11a + a = -10a -10a - 3 b – 9b= -8b If there is no # in front of a variable it is a understood 1

Simplify the expression A) Simplify the expression 6x + 5y² - y²= 4y² + 6x 1 5y² - 1y² = 4y² B) Evaluate your answer for the given values 4y² + 6x X = 5, y = 3 4(3)² + 6 (5) 4(9) + 6(5) 36 + 30 = 66

Simplify the expression A) Simplify the expression 5bc + 3c² + c²= 1 5bc + 4c² 3c² + 1c² = 4c² B) Evaluate your answer for the given values 5bc + 4c² b = 3, c = 2 5(3)(2) + 4(2)² 15(2) + 4(4) 30 + 16 = 46

Simplifying with Distributive Property Distributive Property: multiplying coefficient by what’s inside ( )’s to simplify Example 3(5+6) Distributive Property: Means to share the outside number with everything on the inside by multiplying 3 x 5 = 15 3 x 6 = 18 15 + 18 = 33 3(2x + 3) 3 x 2x = 6x 3 x 3 = 9 6x + 9

Simplifying with Distributive Property 3(2x + 4x²) + 5 (2x² + 5x) 3 ( 2x)= 6x + 5 ( 2x²)= 10x² 3 ( 4x²)= 12x² + 5 (5x) = 25x 6x + 12x² + 10x² + 25x = 22x² + 31x Distributive Property: Means to share the outside number with everything on the inside by multiplying

Simplifying with Distributive Property -2m - (2m -1) + 4m -2m -1 (2m -1) + 4m 4(d + 3) + 7d Don’t forget a negative times a negative makes a positive 4(d) + 4(3) 4d + 12 + 7d -2m -2m + 1 + 4m -4m + 1 + 4m 4d + 7d = 11d - 4m + 4m = 0m 11d + 12 1 Distributive Property: Means to share the outside number with everything on the inside by multiplying

Simplifying with Perimeter Write the expression for the perimeter of the polygon shown. Perimeter: Distance around an object 3 P = (x+4) + 3 + (2x) + (2x+1) (x+4) Don’t forget to combine like terms x + 2x +2x = 5x (2x) 4 + 3 + 1 = 8 (2x+1) 5x + 8

Simplifying with Perimeter Write the expression for the perimeter of the polygon shown. Perimeter: Distance around an object P = (2x+1) + (4x) + (3) + (6x+3) (2x +1) (4x) Don’t forget to combine like terms 2x + 4x +6x = 12x (3) (6x + 3) 1 + 3 + 3 = 7 12x + 7

Lesson Quiz Combine like terms. 1. 3x + 4 + 2x 2. 13k + 6  8m + 9 + k Simplify. 3. 4(3x + 6)  7x 4. 6(x + 5) + 3x Solve. 5. The accounting department ordered 15 boxes of pens. The marketing department ordered 9 boxes of pens. If the total cost of the combined order was $72, what is the price of each box of pens? 5x + 4 14k – 8m + 15 5x + 24 9x + 30 $3

Quiz Time!! Open Your books to Page 15 Quiz # 24, 28, 30, 32, 52 Homework # 23, 25, 27, 31, 51