The document discusses the distributive property and how it is used to simplify algebraic expressions. It provides examples of distributing terms over addition and subtraction, such as 5(x + 7) = 5x + 35. It also discusses like terms and how they can be combined when simplifying expressions.

1. Section 1.5 Distributive Property The students will be able to use the distributive property to simplify expressions.

2. The Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside. a(b + c) = ab + ac and (b + c) a = ba + ca a(b - c) = ab - ac and (b - c) a = ba - ca Example #1 5(x + 7) 5 • x + 5 • 7 5x + 35

3. Example #2 3(m - 4) 3 • m - 3 • 4 3m - 12 Example #3 -2(y + 3) -2 • y + (-2) • 3 -2y + (-6) -2y - 6

4. Which statement demonstrates the distributive property incorrectly ? 3(x + y + z) = 3x + 3y + 3z (a + b) c = ac + bc 5(2 + 3x) = 10 + 3x 6(3k - 4) = 18k - 24 Answer Now

5. A term is a 1) number, 2) variable, or 3) a product / quotient of numbers and variables. Example 5 m 2x 2

6. The coefficient is the numerical part of the term. Examples 1) 4a 4 2) y 2 1 3)

7. Like Terms are terms with the same variable AND exponent. To simplify expressions with like terms, simply combine the like terms.

8. Are these like terms? 1) 13k, 22k Yes, the variables are the same . 2) 5ab, 4ba Yes, the order of the variables doesn’t matter. 3) x 3 y, xy 3 No, the exponents are on different variables.

9. Which of the following is the simplified form of -4x + 7x ? -4 3x -3x 4 Answer Now

10. The above expression simplifies to: 5a and a are like terms and are like terms

11. 12a 2) 6.1y - 3.2y 2.9y 3) 4x 2 y + x 2 y 5x 2 y 4) 3m 2 n + 10mn 2 + 7m 2 n - 4mn 2 10m 2 n + 6mn 2 Simplify 1) 5a + 7a

12. 21a + 6b 6) 4d + 6a 2 - d + 12a 2 18a 2 + 3d 5) 13a + 8a + 6b 7) y

13. Which of the following is the simplified form of 5x - 4 - 7x + 14 ? -12x + 10 -2x + 10 2x - 18 12x – 18 Answer Now

14. If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle? 4x - 2 4x + 2 5x - 2 5x - 7 Answer Now

15. Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles? Answer Now

16. Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ? -36 3a - 36 8a - 36 8a + 36 Answer Now