Algebraic Expressions Unit 7 Expanding and Factoring Algebraic
Algebraic Expressions
Unit 7 – Expanding and Factoring Algebraic Expressions
Vocabulary Factor (verb) - To express as a product of two or more factors Distributive Property - A property of real numbers that states that the product of the sum or difference of two numbers is the same as the sum or difference of their products. Example: Multiplication over addition 2(15 + 4) = 2 × 15 + 2 × 4 Multiplication over subtraction 3(5 – 8) = 3 × 5 – 3 × 8
Expanding Algebraic Expressions Bar Model Example Expand each expression. 3(f + 2) means 3 groups of (f + 2) 3 f + 6
Expanding Algebraic Expressions Distributive Property Example Expand each expression. 3(f + 2) 3 f + 6
Expanding Algebraic Expressions Bar Model Example Expand each expression. 4(g + 4) means 4 groups of (g + 4) 4 g + 16
Expanding Algebraic Expressions Distributive Property Example Expand each expression. 4(g + 4) 4 g +16
Expanding Algebraic Expressions Practice Expand each expression 1. 2(p + 7) 2 p + 14 2. 6(7 m + 9) 42 m + 54 3. 9(d - 4) 9 d - 36 4. 3(9 y – 6) 27 y - 18
Factoring Algebraic Expressions Example Factor each expression. 6 d + 10 1 st – find the greatest common factor of 6 d and 10 GCF = 2 2 nd – divide each term by the GCF 6 d ÷ 2 = 3 d 10 ÷ 2 = 5 3 rd – use the GCF and the quotients to rewrite the expression 2(3 d + 5)
Factoring Algebraic Expressions Example Factor each expression. 8 t + 28 1 st – find the greatest common factor of 8 t and 28 GCF = 4 2 nd – divide each term by the GCF 8 t ÷ 4 = 2 t 28 ÷ 4 = 7 3 rd – use the GCF and the quotients to rewrite the expression 4(2 t + 7)
Factoring Algebraic Expressions Example Factor each expression. 9 i - 27 1 st – find the greatest common factor of 9 i and 27 GCF = 9 2 nd – divide each term by the GCF 9 i ÷ 9 = i 27 ÷ 9 = 3 3 rd – use the GCF and the quotients to rewrite the expression 9(i - 3)
Factoring Algebraic Expressions Practice Factor each expression 1. 24 g + 8 8(3 g + 1) 2. 45 h + 5 5(9 h + 1) 3. 21 b - 7 7(3 b - 1) 4. 56 z – 14 14(4 z - 1)
Expanding and Factoring Algebraic Expressions Mixed Practice State whether each pair of expressions is equivalent 1. 6(2 u + 3) and 6 u + 18 12 u + 18 and 6 u + 18 no 3. 22 s + 18 and 2(11 s + 9) yes 2. 3(2 h - 5) and 6 h -15 4. 6 h + 15 and 3(2 h - 5) 6 h - 15 and 6 h - 15 3(2 h + 5) and 3(2 h - 5) yes no
Simplifying and Factoring Algebraic Expressions Practice Simplify each expression. Then Factor the expression 1. 9 g + 19 + 4 g + 7 13 g + 26 13(g + 2) 2. 9(6 a + 7) – 6 – 3 a 54 a + 63 – 6 – 3 a 51 a + 57 3(17 a + 19)
- Slides: 14