Common Algebraic Expressions

This handout contains common algebraic expressions that can help guide you through formulas and algebraic concepts. For additional assistance with Algebra, make an appointment with an AAC Tutor.

Addition and Subtraction of Addition of Real Properties of Addition Fractions Numbers Commutative Property of Addition 푎 푐 푎+푐 (+3) + (+4) = +7 + = b ≠ 0 a + b = b + a 푏 푏 푏 (-3)+(-4)= -7 Associative Property of Addition 푎 푐 푎−푐 - = b ≠ 0 (a + b) + c = a + (b + c) 푏 푏 푏 (-3)+(+4)= +1

Properties of Multiplication (+3)+(-4)= -1 Strategy for Solving Word Problems

Commutative Property of Multiplication Step 1 Read the problem carefully to ab = ba determine what you are being asked to find.

Associative Property of Multiplication Step 2 Select a variable to represent each (ab)(c) = (a)(bc) unknown quantity. Specify precisely what each variable represents, and note any Function Notation restrictions on each variable. The function notation f(x) is read “f of x.” Step 3 If necessary, make a sketch and translate the problem into a word equation f(x) represents a unique output (range) value for each input or a system of word equations. Then (domain) value of x. f(x) ≠ f ∙ x translate each word equation into an algebraic equation. Δ Greek symbol to represent change Step 4 Solve the equation or system of Slope = m equations, and answer the question completely in the form of a sentence. Two points on a line (x1,y1) (x2,y2) Step 5 Check the reasonableness of your y2−y1 Δ푦 m = x1 ≠ x2 m = answer. 푥2−푥1 Δ푥

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Slope-Intercept Form Point-Slope Form Rate Principle y = mx + b y - y1 = m(x - x1) Amount = Rate X Base A= R ∙ B y-intercept = (0, b) passes through the point (x1, y1) with slope Variable Cost = Cost per item X Number of m items 1 y = x + 3 2 Example: Interest = Principle invested X Rate X Time 1 = slope 2 1 Or I = P ∙ R for T = 1 y - 1 = (x - 1) 3 (0, 3) = y- intercept Distance = Rate X Time passes through the point (1, 1) with slope

1 Work = Rate X Time

3 Raising Products and Quotients to a Power Product Rule for Notes ______Exponents m m m 3 2 2 3 2 6 ______(xy) = x ∙ y (3x ) = 3 (x ) = 9x m n m + n x ∙ x = x ______3 2 3 + 2 5 푥 푥 푚 3 32 9 2 ∙ 2 = 2 = 2 = 32 ______( )m = ( )2 = = 푦 푦푚 푥3 (푥3) 푥6 ______Power Rule for ______Exponents ______(xm)n = xmn ______3 2 3(2) 6 (2 ) = 2 = 2 = 64 ______Exponential Notation Zero Exponents ______n y 0 b = b ∙ b ∙ b… n times x = x ∙ x ∙ x… x times X = 1 ______125420 = 1 4 3 ______2 = 2 ∙ 2 ∙ 2 ∙ 2 = 16 5 = 5 ∙ 5 ∙ 5 = 125 0 5 = 1 ______0 0 x + y = 1 + 1 = 2 ______Quotient Rule for Negative Exponents Fraction to a Negative ______Exponents Exponent ______1 x-n = ______푥푚 푥푛 푥 푦 m - n ( )-n = ( )n ______푛 = x 푦 푥 푥 1 1 -2 ______3 = 2 = 24 3 9 4 -3 5 3 ______= 24 - 2 = 22 = 4 ( ) = ( ) 22 5 4 ______Hall, James W., and Brian A. Mercer. Beginning and Intermediate Algebra: The Language and Symbolism of Mathematics. New York: McGraw-Hill, 2011. Print.

Academic Achievement Center For additional help with Algebra, make an appointment with an AAC tutor. Tamarack 2nd Floor 588-5088 Columbia College