AlgebraMenu1Why You Need Algebra2What Is Algebra?3How to Add and Subtract Variables4How to Multiply Numbers with Variables5Examples of Multiplying Numbers with Variables6What Are Variable Terms?7How to Expand Parentheses with Variables8How Do You Multiply Parentheses?9What Are the Parentheses Rules? On this page, we can see all the rules for parentheses in one spot. Rule Parentheses (a + b) (c + d) = a ⋅ c + a ⋅ d + b ⋅ c + b ⋅ d a + (c + d) = a + c + d a −(c + d) = a − c − d a ⋅(b + c) = a ⋅ b + a ⋅ c (a + b) (c + d) = a ⋅ c + a ⋅ d + b ⋅ c + b ⋅ d a + (c + d) = a + c + d a −(c + d) = a − c − d a ⋅(b + c) = a ⋅ b + a ⋅ c Note! Remember to write the terms in descending order! Then it will look like this: 2x3 − 4x2 + 5x − 3 2x3 − 4x2 + 5x − 3 Example 1 Evaluate x + (−2x + 5) x + (−2x + 5) = x − 2x + 5 = −x + 5 Example 2 Evaluate 4 −(12 − 3x2) 4 −(12 − 3x2) = 4 − 12 + 3x2 = 3x2 − 8 Example 3 Evaluate −4x2 (2 − x) − 4x2 (2 − x) = −8x2 + 4x3 = 4x3 − 8x2 Example 4 Evaluate (x + 1) (x − 2) = (x + 1) (x − 2) = x2 − 2x + x − 2 = x2 − x − 2 (x + 1) (x − 2) = x2 − 2x + x − 2 = x2 − x − 2 Example 5 Evaluate (3x2 + y) (2 − x) = (3x2 + y) (2 − x) = 6x2 − 3x3 + 2y − xy = −3x3 + 6x2 − xy + 2y (3x2 + y) (2 − x) = 6x2 − 3x3 + 2y − xy = −3x3 + 6x2 − xy + 2y Example 6 Evaluate (2x + 3) (4x − 5) = (2x + 3) (4x − 5) = 2x ⋅ 4x + 2x ⋅(−5) + 3 ⋅ 4x + 3 ⋅(−5) = 8x2 + (−10x) + 12x − 15 = 8x2 + 2x − 15 (2x + 3) (4x − 5) = 2x ⋅ 4x + 2x ⋅(−5) + 3 ⋅ 4x + 3 ⋅(−5) = 8x2 + (−10x) + 12x − 15 = 8x2 + 2x − 15 Want to know more?Sign UpIt's free!DoneContinue10What Are the Power Rules for Variables?11How to Divide Powers12How to Multiply Powers in Parentheses13Examples of Solving Powers with Variables14What Is the Connection Between Powers and Roots?15How to Simplify Fractions with Variables16How to Multiply Fractions with Variables17How to Divide Fractions by Canceling18How to Add and Subtract Fractions with x in the Denominator19How to Factor Variable Expressions20How to Factorize and Simplify Fractions with Variables21How to Factorize Polynomials of Degree 3 and 422How are Rational Expressions Simplified?23The First Algebraic Identity of Quadratic Expressions24The Second Algebraic Identity of Quadratic Expressions25The Third Algebraic Identity of Quadratic Expressions26What Is the Formula for Completing the Square?27Why You Need Equations28What Is an Equation?29What Is a Variable?30How to Solve Equations (Change Sides, change sign)31How to Get Rid of the Number in Front of x32How to Solve Linear Equations (Combined Methods)33How to Get Rid of the Number Under x34How to Solve Equations with Parentheses35How to Solve Formulas for Specified Variables36How to Solve Quadratic Equations Without a Linear Term37How to Solve Quadratic Equations38How to Factorize Quadratic Expressions39What Is Polynomial Long Division?40How to Solve Cubic and Quartic Equations41What Are Systems of Equations?42Graphic Representation of Equations43How to Graphically Solve Systems of Equations44Solve Systems of Equations with the Substitution Method45Solve Systems of Equations with the Elimination Method46How to Solve Systems of Nonlinear Equations47Solve Systems of Equations with Multiple Unknowns48How to Solve Equations with Fractions49Solve Rational Equations with x in the Denominator50What Are Radical Equations?51What Are Power Equations?52How to Check Solutions to an Equation53How to Formulate an Equation Representing a Problem54What Is the Zero Product Property?55How to Solve Equations Using Substitution56How to Solve Equations by Graphing57How to Solve a Linear Inequality58How to Solve Inequalities Graphically59How Do Sign Charts Work?60How to Find the Interval of an Inequality61What Are Quadratic Inequalities?62How to Solve Inequalities of Degree 3 or More63What Are Rational Inequalities?64What Is a Logarithm?65What Is Euler's Number e?66What Is the Natural Logarithm?67What Are the Logarithm Rules?68What Are Exponential Equations?69What Are Logarithmic Equations?70How to Solve Exponential Inequalities71How to Solve Logarithmic Inequalities
On this page, we can see all the rules for parentheses in one spot. Rule Parentheses (a + b) (c + d) = a ⋅ c + a ⋅ d + b ⋅ c + b ⋅ d a + (c + d) = a + c + d a −(c + d) = a − c − d a ⋅(b + c) = a ⋅ b + a ⋅ c (a + b) (c + d) = a ⋅ c + a ⋅ d + b ⋅ c + b ⋅ d a + (c + d) = a + c + d a −(c + d) = a − c − d a ⋅(b + c) = a ⋅ b + a ⋅ c Note! Remember to write the terms in descending order! Then it will look like this: 2x3 − 4x2 + 5x − 3 2x3 − 4x2 + 5x − 3 Example 1 Evaluate x + (−2x + 5) x + (−2x + 5) = x − 2x + 5 = −x + 5 Example 2 Evaluate 4 −(12 − 3x2) 4 −(12 − 3x2) = 4 − 12 + 3x2 = 3x2 − 8 Example 3 Evaluate −4x2 (2 − x) − 4x2 (2 − x) = −8x2 + 4x3 = 4x3 − 8x2 Example 4 Evaluate (x + 1) (x − 2) = (x + 1) (x − 2) = x2 − 2x + x − 2 = x2 − x − 2 (x + 1) (x − 2) = x2 − 2x + x − 2 = x2 − x − 2 Example 5 Evaluate (3x2 + y) (2 − x) = (3x2 + y) (2 − x) = 6x2 − 3x3 + 2y − xy = −3x3 + 6x2 − xy + 2y (3x2 + y) (2 − x) = 6x2 − 3x3 + 2y − xy = −3x3 + 6x2 − xy + 2y Example 6 Evaluate (2x + 3) (4x − 5) = (2x + 3) (4x − 5) = 2x ⋅ 4x + 2x ⋅(−5) + 3 ⋅ 4x + 3 ⋅(−5) = 8x2 + (−10x) + 12x − 15 = 8x2 + 2x − 15 (2x + 3) (4x − 5) = 2x ⋅ 4x + 2x ⋅(−5) + 3 ⋅ 4x + 3 ⋅(−5) = 8x2 + (−10x) + 12x − 15 = 8x2 + 2x − 15 Want to know more?Sign UpIt's free!DoneContinue
