2. WARMUPS 1.3XY + 4XY – 6X + 8X + 5 2.(2XY)(4XY) + (4XY)(7XY) 3. 6X – 5X + 3X + 9Y – 3Y 4.(3X)(3X)(3X)(3X) 5.DRAW A FROG

3. HOMEWORK IF YOU CAN DO THESE YOU ARE A SUPER MATHEMATICIAN

4. The Distributive Property & Combining Like Terms

6. T HE D ISTRIBUTIVE P ROPERTY a(b + c) = ab + ac (b + c)a = ba + ca 2(x + 5) 2(x) + 2(5)2x + 10 (x + 5)2(x)2 + (5)2 2x + 10 (1 + 5x)2(1)2 + (5x)2 2 + 10x y(1 + x) y(1) +y(x) y + xy U SING THE D ISTRIBUTIVE P ROPERTY = = = = = = = = The product of a and (b + c): BACK

7. –(y – 5) = (y)(–1) + (–5)(–1) = –y + 5 –(7 – 3x) = (–1)(7) + (–1)(–3x) = –7 + 3x = –3 – 3x (–3)(1 + x)= (–3)(1) + (–3)(x) Simplify. Distribute the –3. Simplify. Distribute the –1. Simplify. –a = –1 a U SING THE D ISTRIBUTIVE P ROPERTY Remember that a factor must multiply each term of an expression. Forgetting to distribute the negative sign when multiplying by a negative factor is a common error. BACK

8. Like Terms are expressions that contain the same variable raised to the same power like 4mn and 7mn. Combine like terms. S IMPLIFYING BY C OMBINING L IKE T ERMS 4x 2 + 2 + x 2 - 6 = 11x +y The 8x and 3x are like terms and can be combined. 8x + 3x + y = 4x 2 +1 x 2 + 2 - 6 Group like terms. = 5x 2 - 4 BACK

10. Combine like terms with parenthesis… BACK

11. Objectives Use the Distributive Property to solve equations. Solve real-world problems by using multistep equations.

12. Key Skills Solve 3(x - 4) = 48 Use the distributive property. 3 * x + 3 * -4 = 48 Solve 3(x - 4) = 48 Multiply 3x - 12 = 48 Add both sides of the = sign. +12 3x = 60 Divide both sides of the = sign by 3. 3 x = 20

13. Key Skills Solve 5(x +2) = 35 Use the distributive property. 5 * x + 5 * 2 = 35 Solve 5(x +2) = 35 Multiply 5x + 10 = 35 Subtract 10 from both sides of the = sign. -10 5x = 25 Divide both sides of the = sign by 3. 5 x = 5 TRY THIS

14. Key Skills Solve 3y – 8 –y = 6 Combine like terms that are on the same side of the = sign. Solve 3y – 8 –y = 6 2y – 8 = 6 Add 8 to both sides of the = sign. + 8 2y = 14 Divide both sides of the equal sign by 2 2 y = 7

15. Key Skills Solve 6y +2 –3y = 8 Combine like terms that are on the same side of the = sign. Solve 6y +2 –3y = 8 3y +2 = 8 Subtract 2 from both sides of the = sign. -2 3y = 6 Divide both sides of the equal sign by 3 3 y = 2 TRY THIS

16. Key Skills Solve 4x -8(x + 1) = 8 Distribute -8 4x -8 * x + -8 * 1 = 8 Multiply 4x -8x -8 = 8 Combine like terms. 4x -8x -8 = 8 -4x -8 = 8 Add 8 to both sides of the = sign. +8 +8 -4x = 16 Divide both sides of the equal sign by -4 -4 x = -4

17. Key Skills Use the Distributive Property to solve multistep equations. Solve 8x – 2(3x – 4) = 5x – 7. 8x + (–2)(3x) + (–2)(–4) = 5x – 7 8x – 6x + 8 = 5x – 7 Distributive -2 Solve 8x – 2(3x – 4) = 5x – 7. Multiply. 8x – 6x + 8 = 5x – 7 Combine like terms that are on the same side of the = sign. 2x + 8 = 5x – 7

18. Subtract 2x from both sides of the = sign. -2x 8 = 3x -7 Add 7 to both sides of the = sign. +7 15 = 3x Divide both sides of the = sign by 3 3 5 = x

19. Key Skills Use the Distributive Property to solve multistep equations. Solve 4y – 7(y +6) = 5y – 2. 4y + (–7)(y) + (–7)(+6) = 5y – 2 4y – 7y -42 = 5y – 2 Distributive -7 Solve 4y – 7(y +6) = 5y – 2. Multiply. 4y – 7y -42 = 5y – 2 Combine like terms that are on the same side of the = sign. -3y -42 = 5y – 2 TRY THIS

20. -3y -42 = 5y – 2 Add 3y to both sides of the = sign. +3y -42 = 8y -2 Add 2 to both sides of the = sign. +2 -40 = 8y Divide both sides of the = sign by 8 8 -5 = y

21. The Distributive Property & Combining Like Terms BACK

22. HOMEWORK; IF YOU CAN DO THESE YOU ARE A SUPER MATHEMATICIAN

23. EXPRESSIONS MONDAY - BRING CALCULATORS

24. REVIEW MATHEMATICS; TIME TRIAL FOUR DESCRIBE: COEFFICIENT, VARIABLES, CONSTANT

25. REVIEW 1: USE THE DISTRIBUTIVE PROPERTY TO REWRITE 4A ( – 3A 2 + 5A 3 )

26. REVIEW 2: REWRITE THE EXPRESSION 6S 2 ( - 5S 2 + 2S 2 )

27. REVIEW 3: SIMPLIFY: 5AR + 6AR 2 + 7AR 2 + 3AR

28. REVIEW 4: SIMPLIFY: 5AR 2 · 5AR 2 · 5AR 2 + 5AR

29. REVIEW 5: SIMPLIFY: (5XY 2 )(3XY 2 - 2XY + X)

30. REVIEW 6: COMBINE THE TERMS 5S + 3Y - G + 19 – S - G - 2

31. REVIEW 7 :SIMPLIFY (3AB · 4AB) + (2AB · 6AB)

32. REVIEW 8: SIMPLIFY FOR A = 4, B = 5, C = 6 -4AB 3 C

33. REVIEW 9: SIMPLIFY: (X 2 Y)(X 2 Y)

34. REVIEW 10: SIMPLIFY (2AB 2 +2AB - 2A) – (3AB 2 – 3AB + A)

35. REVIEW 11: USE THE DISTRIBUTIVE PROPERTY -B ( -A - B - C)

36. REVIEW 12: SIMPLIFY (AB) (AB) (AB) (AB) + (AB)

37. REVIEW 13: SIMPLIFY M + 36 + 48 - 2M

38. REVIEW 14: 4AB 2 + 5AB 2 - 3AB + 9AB 2

39. REVIEW 15: 2G 2 · 2G 2 + 2G + 2G

40. REVIEW 16: 150 + 10R - 5R - 50

41. HOMEWORK CATTLE HANDOUT IF YOU CAN DO THESE YOU ARE A SUPER MATHEMATICIAN