1.4 Basic Rules of Algebra

Terms terms – parts of an algebraic expression separated by addition (or subtraction) signs Ex: 2x + 5 2x (2 times x) 2 terms 2 is the “coefficient” or # part 5 is a “constant” (no variable)

Properties commutative property of addition a + b = b + a Ex: 2 + 3 = 3 + 2 commutative property of multiplication a ∙ b = b ∙ a Ex: 2 ∙ 3 = 3 ∙ 2 (we can change the order when we add or mult. without changing the result)

associative property of addition (a + b) + c = a + (b + c) Ex: (2 + 3) + 4 = 2 + (3 + 4) associative property of multiplication (a ∙ b) ∙ c = a ∙ (b ∙ c) Ex: (2 ∙ 3) ∙ 4 = 2 ∙ (3 ∙ 4) 6 ∙ 4 = 2 ∙ 12 24 = 24 (we can change the grouping of #s when we add or mult. w/o changing the result)

distributive property 5 I II 3 4 Total Area = Area I + Area II 5(3 + 4) = 5(3) + 5(4) 5(7) = 15 + 20 35 = 35

distributive property a(b + c) = ab + ac a(b – c) = ab – ac Ex: 3(r + 2) = 3(r) + 3(2) = 3r + 6 (2x + 7)4 = 4(2x) + 4(7) = 8x + 28

7(x + y – 2) = 7(x) + 7(y) – 7(2) = 7x + 7y – 14

Simplifying an Algebraic Expression like (or similar) terms – 2 or more terms with the same variables raised to the same powers Ex: terms like terms? 3x, 4x 2a2b, -7a2b ½x2y, 13xy2 5, 8m, 12m

Ex: terms like terms? 3x, 4x yes 2a2b, -7a2b yes ½x2y, 13xy2 no 5, 8m, 12m no

simplify – reduce the # of terms in an expression Ex: Simplify by combining like terms (a) 5x + 2x = (5 + 2)x = 7x (b) 13y – 7y = (13 – 7)y = 6y to combine like terms, just add/sub. the coefficients If there are ( ), use the distributive property first

Ex: Simplify (a) 13a + 15 + 2a + 11 = 13a + 2a + 15 + 11 = 15a + 26 (b) 2(4x + 3) – 5 = 2(4x) + 2(3) – 5 = 8x + 6 – 5 = 8x + 1