Simplifying Complex Fractions

Factor Expressions with Fractional Exponents

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √27

In Exercises 83–90, perform the indicated operation or operations. (3x+4y)^2−(3x−4y)^2

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. A number decreased by the sum of the number and four 

Intersection of Sets, Union of Sets and Venn Diagrams

In Exercises 29–34, find the union of the sets. {e,m,p,t,y} ∪ ∅

Quotient Rule for Radicals

In Exercises 83–90, evaluate each expression without using a calculator. 27^(1/3)

In Exercises 15–58, find each product. (x−1)(x+2)

Understanding Exponents and Their Operations

Use the quotient rule to simplify the expressions in Exercises 45-46. √(121/4)

Factoring Perfect Square Trinomials - Ex1

Absolute Value for Beginners

Mathematical Models - Worked example 3

Simplifying Square Roots

Evaluate multiple step algebraic expressions by substitution

Simplify by reducing the index of the radical : [y^3]^(1/6)

How To Evaluate Expressions With Variables Using Order of Operations

In Exercises 33–44, add or subtract terms whenever possible. 3√8−√32+3√72−√75

Simplifying radicals - High powered roots

Simplifying Radical Expressions Involving Variables - Example 1

Using Quotient Rule to Write as a Single Radical 

In Exercises 91–100, simplify using properties of exponents. (3y^1/4)^3/y^1/12

In Exercises 33–44, add or subtract terms whenever possible. 4√13x−6√13x

In Exercises 65–76, write each number in decimal notation without the use of exponents. −3.14×10^−3

All about DIVIDING SQUARE ROOTS

Simplify each exponential expression in Exercises 23–64. (−4/x)^3

Simplifying Complex Fractions - Ex 3

In Exercises 61–66, evaluate each algebraic expression for x=2 and y=-5. |x|+|y|

In Exercises 49–56, factor each perfect square trinomial. x^2−14x+49

Factoring Trinomials : Factor by Grouping - ex 3

Adding and Subtracting Rational Expressions

In Exercises 77–86, write each number in scientific notation. 0.0083

Finding all the Zeros of a Polynomial - Example 1

In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (y^2+7y−18)/(y^2−3y+2)

Rational Expressions: Writing in Lowest Terms - Ex 2

How to Simplify an Expression

In Exercises 15–32, multiply or divide as indicated. (x+5)/7 ÷ (4x+20)/9

Factoring by Grouping - Ex 1

Factoring Perfect Square Trinomials - Ex3

In Exercises 21–28, find the intersection of the sets. {s,e,t}∩{t,e,s}

In Exercises 65–76, write each number in decimal notation without the use of exponents. −8.17×10^6

Simplifying Expressions with Negative Exponents - Ex 1

In Exercises 15–58, find each product. (x+5)(x−5)

Simplify each complex rational expression. (1/x-1/2)/(1/3-x/6)

Factoring by Grouping

Simplifying Complex Fractions - Ex 1

Polynomials: Adding, Subtracting, Multiplying and Simplifying - Example 3

Simplify an Algebraic Expression by Combining Like Terms

Mathematical Models - Worked example 2

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √48x^3/√3x

Lesson: Factoring a Sum or Difference of Cubes

In Exercises 77–86, write each number in scientific notation. −3829

In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (6.1×10^−8)(2×10^−4)

Evaluate each exponential expression in Exercises 1–22. 2^2⋅2^3

Exponent Rules: The Power to Power Rule!

Rational Expressions:  Adding and Subtracting.  Ex 1

In Exercises 65–92, factor completely, or state that the polynomial is prime. x^3+2x^2−9x−18

Simplify each exponential expression: (-5x^3y^2)(-2x^(-11)y^(-2))

Multiplying Polynomials - Slightly Harder Examples #6

Simplify Square Roots of Perfect Squares:  Square Root of 81 & (121/144), Negative Square Root of 64

Simplify the algebraic expression. (1/5)(5x) + [(3y) + (- 3y)] - (-x)

In Exercises 83–90, perform the indicated operation or operations. (2x−7)^5/(2x−7)^3

❖ Finding all the Zeros of a Polynomial - Example 3 ❖

Rational Expressions:  Multiplying and Dividing.  Ex 1

In Exercises 103–114, factor completely. (x+y)^4−100(x+y)^2

Set Theory: Types of Sets, Unions and Intersections

Simplify each rational expression. Also, list all numbers that must be excluded from the domain. [x^3+2x^2]/[x+2]

Evaluate each exponential expression in Exercises 1–22. 2^3/2^7

Applying the Rules of Exponents - Basic Examples #1

Simplify the algebraic expression. 5(2x - 3) + 7x

In Exercises 75–82, add or subtract terms whenever possible. √3+³√15

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Eight decreased by three times the sum of a number and six

Adding and Subtracting Polynomials

In Exercises 65–92, factor completely, or state that the polynomial is prime. 5x^3−45x

Simplify algebraic expressions by combining like terms and applying the distributive property

In Exercises 35–38, list all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. {-9, -4/5, 0, 0.25, √3, 9.2, √100}

In Exercises 111–120, use the order of operations to simplify each expression. 10^2−100÷5^2⋅2−3

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 4+5(x-7)^3, for x =9

In Exercises 51–60, rewrite each expression without absolute value bars. ||-3|-|-7||

State the name of the property illustrated: 3+17 = 17+3

Simplify each complex rational expression. [3-1/(x+3)]/[3+1/(x+3)]

Absolute Value and Evaluating Numbers

Use FOIL Method to Multiply Polynomials Algebra

In Exercises 33–68, add or subtract as indicated. (3x+2)/(3x+4) + (3x+6)/(3x+4)

Multiply polynomials using distributive property

Power of a Quotient Property

Power of a Product Property

Simplifying Roots with Higher indexes

Multiplying Variables with Rational Exponents - Basic Example 1

Evaluating Expressions Involving Absolute Value - Example 1

In Exercises 1–10, factor out the greatest common factor. 3x^2+6x

In Exercises 67–82, find each product. (3x−y)(2x+5y)

In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3

In Exercises 65–92, factor completely, or state that the polynomial is prime. 6x^2−6x−12

Radicals - Notation and Simplifying - Radical and Exponential Notation

Factor completely, or state that the polynomial is prime. x^2-11x+28

In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x−1)/(x^2+11x+10)

Distinguish between rational and irrational numbers

In Exercises 65–92, factor completely, or state that the polynomial is prime. 2x^3−8a^2 x+24x^2+72x

Simplifying Expressions with Negative Exponents - Ex 2

In Exercises 5–8, find the degree of the polynomial. 3x^2−5x+4

Radical Notation and Simplifying Radicals

Evaluate each exponential expression in Exercises 1–22. 3^8/3^4

In Exercises 15–58, find each product. (7x^3+5)(x^2−2)

Perform the indicated operation and write the answer in decimal notation. (3*10^3)(1.3*10^2)

In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (−6x^3+5x^2−8x+9)+(17x^3+2x^2−4x−13)

Perform Operations with Polynomials of Several Variables

Comparing Integers Video Lesson

Factor an expression: taking out the greatest common factor

Intersection of Sets

Evaluate each exponential expression in Exercises 1–22. 4^−3

Multiplying Polynomials - Slightly Harder Examples  #1

In Exercises 51–60, rewrite each expression without absolute value bars. |12 - π|

Simplify expressions with 0 and negative exponents

Factor completely, or state that the polynomial is prime. 15x^3+3x^2

Factoring Expressions with Rational Exponents

Simplifying expressions using the Laws of Exponents

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Six times the product of negative five and a number

Real Numbers Introduction

In Exercises 15–32, multiply or divide as indicated. (x^2+x)/(x^2−4) ÷ (x^2−1)/(x^2+5x+6)

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. x^2−14x+45

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 2 and 17

In Exercises 47 - 49, add or subtract terms whenever possible. 7√5 + 13√5

Introduction to Polynomials

Find absolute value using a number line

Simplify each exponential expression in Exercises 23–64. (−3x^2 y^5)^2

Simplify each exponential expression in Exercises 23–64. x^−5⋅x^10

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between the product of six and a number and negative two times the number

Simplify each exponential expression: (-2x^4y^3)^3

Determine the union of two subsets

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 30/40−3/4 □ 14/15⋅15/14

Negative Exponents

In Exercises 97–102, write each algebraic expression without parentheses. 1/3(3x)+[(4y)+(−4y)]

Factor completely, or state that the polynomial is prime. 64-x^2

Subtract polynomials by combining like terms and using integer operations

Multiplying binomials in two variables

Multiply polynomials using a box

Simplify each exponential expression in Exercises 23–64. (3x^4/y)^−3

Factor an expression using the diamond and box method

Write each number in decimal notation: 7.45*10^(-5)

Multiply numbers expressed in scientific notation

Factoring Sum and Difference of Cubes

Polynomial... or NOT?! Recognizing Polynomials, the degree and some Terminology

Simplifying Algebraic Expressions With Parentheses & Variables - Combining Like Terms - Algebra

Evaluate each exponential expression in Exercises 1–22. −2^6

Some Stupid Math Mistakes

In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x−2) ÷ (x+2)/(4x−8)

In Exercises 51–60, rewrite each expression without absolute value bars. |7 - π|

The commutative property

Rationalize the denominator

Power of a Quotient Rule

Finding the Domain of an Expression Involving Fractions - Example 3

Applying the Rules of Exponents - Basic Examples #3

Factoring Trinomials by Trial and Error - Ex 2

Simplifying Radical Expressions Involving Variables - Example 2

In Exercises 15–58, find each product. (5−7x)(5+7x)

How to Find Restrictions on Rational Expressions

Algebra - Complex Fractions

In Exercises 75–84, state the name of the property illustrated. 6+(2+7)=(6+2)+7

Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √24x^4/√3x

Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∩ B.

Simplify each exponential expression in Exercises 23–64. (−5x^4 y)(−6x^7 y^11)

Multiply or divide as indicated. [(x^2+6x+9)(x+3)]/[(x^2-4)(x-2)]

In Exercises 111–120, use the order of operations to simplify each expression. 6(−4)−5(−3)/(9−10)

Factor: using factor sums

GED Sample Test with Solutions , Question #42

Factoring the Difference of Two Squares - Ex 3

Mathematical Models - Worked example 1

In Exercises 57–64, factor using the formula for the sum or difference of two cubes. x^3+64

Multiplying Binomials by the FOIL Method

Divide exponential expressions (part 2)

How to Multiply Binomials

Factoring the Difference of Two Squares - Ex 1

In Exercises 35–38, list all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. {-11, -5/6, 0, 0.75, √5, π, √64}

In Exercises 101–108, simplify by reducing the index of the radical. ¹²√x^4y^8

In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (2.4×10^−2)/(4.8×10^-6)

In Exercises 77–86, write each number in scientific notation. 579,000,000,000,000,000

Simplify expressions with 0 and negative exponents 

Factoring a sum or difference of two cubes

Rationalizing the denominator with a radical

Subtracting rational expressions

In Exercises 11–16, factor by grouping. x^3−3x^2+4x−12

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. x^2+8x+15

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √125x^2

Simplify exponential multiplication expressions

Simplify each exponential expression in Exercises 23–64. x^14/x^7

Absolute Value - Basic Examples

In Exercises 65–92, factor completely, or state that the polynomial is prime. x^3+2x^2−4x−8

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x^2-6x+3, for x=7

Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (-6x^3+7x^2-9x+3)+(14x^3+3x^2-11x-7)

In Exercises 91–100, simplify using properties of exponents. (25x^4y^6)^1/2

In Exercises 47 - 49, add or subtract terms whenever possible. 4√72 - 2√48

In Exercises 85–96, simplify each algebraic expression. 5(3y−2)−(7y+2)

Venn Diagrams: Shading Regions with Three Sets, Part 2 of 2

Evaluating Numbers Raised to Fractional Exponents

In Exercises 83–90, evaluate each expression without using a calculator. 16^(−6/2)