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Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
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Multiplying Polynomials

In this section you will learn how to multiply any two polynomials.

Multiplying Monomials with the Product Rule

To multiply two monomials, such as x3 and x5, recall that

x3 = x · x · x  and  x5 = x · x · x · x · x,


The exponent of the product of x3 and x5 is the sum of the exponents 3 and 5. This example illustrates the product rule for multiplying exponential expressions.


Product Rule

If a is any real number and m and n are any positive integers, then

am · an = am + n.


Multiplying monomials

Find the indicated products.

a) x2 · x4 · x

b) (-2ab)(-3ab)

c) -4x2y2 · 3xy5

d) (3a)2


a) x2 · x4 · x =  x2 · x4 · x1  
  = x7 Product rule
b) (-2ab)(-3ab) = (-2)(-3) · a · a · b · b  
  = 6a2b2 Product rule
c) (-4x2y2)(3xy5) = (-4)(3)x2 · x · y2 · y5
  = -12x3y7 Product rule
d) (3a)2 = 3a · 3a  
  = 9a2  


Be sure to distinguish between adding and multiplying monomials. You can add like terms to get 3x4 + 2x4 = 5x4, but you cannot combine the terms in 3w5 + 6w2. However, you can multiply any two monomials: 3x4 · 2x4 = 6x8 and 3w5 · 6w2 = 18w7.


Multiplying Polynomials

To multiply a monomial and a polynomial, we use the distributive property.

Multiply monomials and polynomials

Find each product.

a) 3x2(x3 - 4x)

b) (y2 - 3y + 4)(-2y)

c) -a(b - c)


Note in part c) that either of the last two binomials is the correct answer. The last one is just a little simpler to read.

Just as we use distributive property to find the product of a monomial and a polynomial, we can use the distributive property to find the product of two binomials as the product of a binomial and a trinomial.


Multiplying polynomials

Use the distributive property to find each product

a) (x + 2)(x + 5)

b) (x + 3)(x2 + 2x - 7)


a) First multiply each term of x + 5 by x + 2:

b) First multiply each term of the trinomial by x + 3:

Products of polynomials can also be found by arranging the multiplication vertically like multiplication of whole numbers.


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