Algebraic Expressions

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Presentation transcript:

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) 3(f + 2) means 3 groups of (f + 2) 3f + 6

Expanding Algebraic Expressions Distributive Property Example Expand each expression. 3(f + 2) 3f + 6

Expanding Algebraic Expressions Bar Model Example Expand each expression. 4(g + 4) 4(g + 4) means 4 groups of (g + 4) 4g + 16

Expanding Algebraic Expressions Distributive Property Example Expand each expression. 4(g + 4) 4g +16

Expanding Algebraic Expressions Practice Expand each expression 2(p + 7) 2p + 14 6(7m + 9) 42m + 54 9(d - 4) 9d - 36 3(9y – 6) 27y - 18

Factoring Algebraic Expressions Example Factor each expression. 6d + 10 1st – find the greatest common factor of 6d and 10 GCF = 2 2nd – divide each term by the GCF 6d ÷ 2 = 3d 10 ÷ 2 = 5 3rd – use the GCF and the quotients to rewrite the expression 2(3d + 5)

Factoring Algebraic Expressions Example Factor each expression. 8t + 28 1st – find the greatest common factor of 8t and 28 GCF = 4 2nd – divide each term by the GCF 8t ÷ 4 = 2t 28 ÷ 4 = 7 3rd – use the GCF and the quotients to rewrite the expression 4(2t + 7)

Factoring Algebraic Expressions Example Factor each expression. 9i - 27 1st – find the greatest common factor of 9i and 27 GCF = 9 2nd – divide each term by the GCF 9i ÷ 9 = i 27 ÷ 9 = 3 3rd – use the GCF and the quotients to rewrite the expression 9(i - 3)

Factoring Algebraic Expressions Practice Factor each expression 24g + 8 8(3g + 1) 45h + 5 5(9h + 1) 21b - 7 7(3b - 1) 56z – 14 14(4z - 1)

Expanding and Factoring Algebraic Expressions Mixed Practice State whether each pair of expressions is equivalent 6(2u + 3) and 6u + 18 12u + 18 and 6u + 18 no 3(2h - 5) and 6h -15 6h - 15 and 6h - 15 yes 22s + 18 and 2(11s + 9) 2(11s + 9) and 2(11s + 9) yes 6h + 15 and 3(2h - 5) 3(2h + 5) and 3(2h - 5) no

Simplifying and Factoring Algebraic Expressions Practice Simplify each expression. Then Factor the expression 9g + 19 + 4g + 7 13g + 26 13(g + 2) 9(6a + 7) – 6 – 3a 54a + 63 – 6 – 3a 51a + 57 3(17a + 19)