1. Fundamental Concepts of Algebra

Perform Operations with Polynomials in Several Variables

Polynomials

Introductory Algebra - Polynomials in Several Variables

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 

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

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)

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

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

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

Multiplying Polynomials - Slightly Harder Examples #6

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

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

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

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

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

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

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

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

Multiplying Polynomials - Slightly Harder Examples  #1

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

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

Introduction to Polynomials

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

Subtract polynomials by combining like terms and using integer operations

Multiplying binomials in two variables

Multiply polynomials using a box

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

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

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

Multiplying Binomials by the FOIL Method

How to Multiply Binomials

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)

Expanding Square Brackets

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

Multiplying Polynomials

Perform the indicated operations. Indicate the degree of the resulting polynomial. (13x^3y^2-5x^2y-9x^2)-(-11x^3y^2-6x^2y+3x^2-4)

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

In Exercises 83–90, perform the indicated operation or operations. (3x+5)(2x−9)−(7x−2)(x−1)

MATHS - Algebra - Polynomials

Polynomials: Adding, Subtracting, Multiplying and Simplifying - Example 2

Multiplying Binomials

In Exercises 5–8, find the degree of the polynomial. x^2−4x^3+9x−12x^4+63

In Exercises 67–82, find each product. (9x+7y)^2

In Exercises 33–68, add or subtract as indicated. (x+9)/10x^3 + 11/15x^2

Classify polynomials

In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (7x^4 y^2−5x^2 y^2+3xy)+(−18x^4 y^2−6x^2 y^2−xy)

In Exercises 15–58, find each product. (9−5x)^2

In Exercises 33–68, add or subtract as indicated. 3/(x+1) − 3/x

How to Multiply Polynomials Properly - Nerdstudy

In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x+5)/(x^2−25)

In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 2x+3x^2−5

Perform the indicated operations. Indicate the degree of the resulting polynomial. (7x^2-8xy+y^2)+(-8x^2-9xy-4y^2)

Add polynomials by combining like terms

Multiplying Multivariable Polynomials

In Exercises 67–82, find each product. (7xy^2−10y)(7xy^2+10y)

Polynomials: Adding, Subtracting, Multiplying and Simplifying - Example 1

In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (3x^4 y^2+5x^3 y−3y)−(2x^4 y^2−3x^3 y−4y+6x)

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

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

Multiplying Polynomials - Slightly Harder Examples # 5 - Cubing Binomials

Prove the Algebraic Squares Proof algebraically

In Exercises 67–82, find each product. (7x^2 y+1)(2x^2 y−3)

In Exercises 15–32, multiply or divide as indicated. (x^3−25x)/4x^2 ⋅ (2x^2−2)/(x^2−6x+5) ÷ (x^2+5x)/(7x+7)

In Exercises 33–68, add or subtract as indicated. 5/x + 3

In Exercises 15–58, find each product. (1−y^5)(1+y^5)

In Exercises 33–68, add or subtract as indicated. 3x/8 + x/12

In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (5x^2−7x−8)+(2x^2−3x+7)−(x^2−4x−3)

In Exercises 15–58, find each product. (x−1)^3

In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x^2+3x−10) ÷ (x^2+5x+6)/(x^2+8x+15)

Multiplying Polynomials - Math Tutorial

Evaluate each algebraic expression for the given value or value(s) of the variable(s). 3+6(x-2)^3 for x=4

In Exercises 15–58, find each product. (4x^2−1)^2

In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. (2x+3)/x

In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (x^2−14x+49)/(x^2−49)

Multiplying Polynomials Example Problem

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

In Exercises 33–68, add or subtract as indicated. (4x^2+x−6)/(x^2+3x+2)−3x/(x+1)+5/(x+2)

Multiplying Polynomials - Slightly Harder Examples # 4 - Cubing Binomials

Special Polynomial Products

In Exercises 15–32, multiply or divide as indicated. (x^3−8)/(x^2−4) ⋅ (x+2)/3x

In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. 7/(x−3)

In Exercises 15–58, find each product. (4x^2+5x)(4x^2−5x)

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

In Exercises 33–68, add or subtract as indicated. 2/5x − (x+1)/4x

In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (3x−9)/(x^2−6x+9)

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

In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (17x^3−5x^2+4x−3)−(5x^3−9x^2−8x+11)

In Exercises 15–32, multiply or divide as indicated. (6x+9)/(3x−15) ⋅ (x−5)/(4x+6)

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

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

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

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College Algebra

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