Bell Work: Use the distributive property to evaluate 4(6 – 2 + 5 – 7)

1. Bell Work: Use the distributive property to evaluate 4(6 – 2 + 5 – 7)

2. Answer: 4(6 – 2 + 5 – 7) = 24 – 8 + 20 – 28 = 16 + 20 – 28 = 36 – 28 = 8

3. Lesson 18: Like Terms, Addition of Like Terms

4. Like terms are terms that have the same variables in the same form or in equivalent forms so that the terms represent the same number regardless of the nonzero values assigned to the variables.

5. Example: In the expression 4xmp – 2pmx + 6mxp Are xmp, pmx, and mxp like terms?

6. Answer: 4xmp – 2pmx + 6mxp Let x = 4, m = 2, and p = 6. Don’t worry about the leading coefficients right now. (4)(2)(6) = 48 (6)(2)(4) = 48 (2)(4)(6) = 48 They are like terms

7. 2 statements regarding like terms • They are in equivalent forms, for they have the same variables in the form of an indicated product, and the order of multiplication of the factors does not affect the value of the product.

8. 2. They represent the same number regardless of the nonzero values assigned to the variables.

9. Addition of like terms: The extension of the distributive property can be rewritten as ba + ca + da + … = (b + c + d + …)a We note that “a” is a common factor of each of the terms on the left and is written outside the parentheses on the right.

10. If we look at the indicated sum of terms 4xmp – 2pmx + 6mxp We see that the factor xmp is a factor of all three terms and can be treated in the same manner as the “a” factor before.

11. Thus, we can rewrite 4xmp – 2pmx + 6mxp As (4 – 2 + 6)xmp = 8xmp The factors of the three variables in the expression 8xmp could be written in any order without changing the value of the expression.

12. To add like terms, we algebraically add the numerical coefficients.

13. Practice: Simplify by adding like terms: 3x + 5 – xy + 2yx – 5x

14. Answer: 3x + 5 – xy + 2yx – 5x = -2x + xy + 5

15. Practice: Simplify by adding like terms: 3xy + 2xyz – 10yx – 5yzx

16. Answer: 3xy + 2xyz – 10yx – 5yzx = -7yx – 3xyz

17. Practice: Simplify by adding like terms: 4 + 7mxy + 5 + 3yxm - 15

18. Answer: 4 + 7mxy + 5 + 3yxm – 15 = -4 + 10mxy

19. Practice: Simplify by adding like terms: 3x – x – y + 5 – 2y – 3x – 10 – 8y

20. Answer: 3x – x – y + 5 – 2y – 3x – 10 – 8y = -x – 11y – 5

21. Practice: Simplify by adding like terms: -3 + xmy – y – 5 + 8ymx – 3y – 14

22. Answer: -3 + xmy – y – 5 + 8ymx – 3y – 14 = -22 – 4y + 9myx

23. HW: Lesson 18 # 1-30 Due Tomorrow