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Arithmetic Operations with Numerical Fractions
Multiplying a Polynomial by a Monomial
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Solving Systems of Equations Using Substitution
Simplifying Fractions 3
Factoring quadratics
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Writing Fractions as Percents
Using Patterns to Multiply Two Binomials
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Example 6
Dividing Monomials
Multiplication can Increase or Decrease a Number
Graphing Horizontal Lines
Simplification of Expressions Containing only Monomials
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Subtracting Polynomials
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Powers of i
Multiplying and Dividing Fractions
Simplifying Complex Fractions
Finding the Coordinates of a Point
Fractions and Decimals
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Solving Equations by Factoring
Slope of a Line
Percent Introduced
Reducing Rational Expressions to Lowest Terms
The Hyperbola
Standard Form for the Equation of a Line
Multiplication by 75
Solving Quadratic Equations Using the Quadratic Formula
Raising a Product to a Power
Solving Equations with Log Terms on Each Side
Monomial Factors
Solving Inequalities with Fractions and Parentheses
Division Property of Square and Cube Roots
Multiplying Two Numbers Close to but less than 100
Solving Absolute Value Inequalities
Equations of Circles
Percents and Decimals
Integral Exponents
Linear Equations - Positive and Negative Slopes
Multiplying Radicals
Factoring Special Quadratic Polynomials
Simplifying Rational Expressions
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Graphuing Linear Inequalities
Linear Functions
Solving Quadratic Equations by Using the Quadratic Formula
Adding and Subtracting Polynomials
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Basic Algebraic Operations and Simplification
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Axis of Symmetry and Vertices
Factoring Polynomials with Four Terms
Evaluation of Simple Formulas
Graphing Systems of Equations
Scientific Notation
Lines and Equations
Horizontal and Vertical Lines
Solving Equations by Factoring
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Adding and Subtracting Rational Expressions with Different Denominators
Adding and Subtracting Fractions
Solving Linear Equations
Simple Trinomials as Products of Binomials
Solving Nonlinear Equations by Factoring
Solving System of Equations
Exponential Functions
Computing the Area of Circles
The Standard Form of a Quadratic Equation
The Discriminant
Dividing Monomials Using the Quotient Rule
Squaring a Difference
Changing the Sign of an Exponent
Adding Fractions
Powers of Radical Expressions
Steps for Solving Linear Equations
Quadratic Expressions Complete Squares
Fractions 1
Properties of Negative Exponents
Factoring Perfect Square Trinomials
Algebra
Solving Quadratic Equations Using the Square Root Property
Dividing Rational Expressions
Quadratic Equations with Imaginary Solutions
Factoring Trinomials Using Patterns
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Subtracting Polynomials

To subtract one polynomial from another, add the first polynomial to the opposite of the polynomial being subtracted.

To find the opposite of a polynomial, multiply each term by -1.

For example:

The opposite of 5x2 is -5x2.

The opposite of -2x + 7 is 2x - 7.

Note:

Here’s a way to find the opposite of a polynomial:

Change the sign of each term.

 

Example 1

Find: (-18w2 + w - 32) - (40 - 13w2)

Solution

Change the subtraction to addition of the opposite.

Remove the parentheses.

Write like terms next to each other.

Combine like terms.

(-18w2 + w - 32) - (40 - 13w2)

= (-18w2 + w - 32) + (-1)(40 - 13w2)

= -18w2 + w - 32 - 40 + 13w2

= -18w2 + 13w2 + w - 32 - 40

= -5w2 + w - 72

So, (-18w2 + w - 32) - (40 - 13w2) = -5w2 + w - 72

Note:

We can also place one polynomial beneath the other and subtract like terms.

To do the subtraction, we change the sign of each term being subtracted, then add.

Example 2

Subtract (15z2 - 5yz2 + 4y3) from (6y3 - 10z3 + 2yz2).

Solution

Be careful! “Subtract A from B” means B - A. The order is important.

Write the difference.

Change the subtraction to addition of the opposite.

Remove the parentheses.

Write like terms next to each other.

Combine like terms.

(6y3 - 10z3 + 2yz2) - (15z2 - 5yz2 + 4y3)

= (6y3 - 10z3 + 2yz2) + (-1) (15z2 - 5yz2 + 4y3)

= 6y3 - 10z3 + 2yz2 - 15z2 + 5yz2 - 4y3

= 6y3  - 4y3 - 10z3 + 2yz2 + 5yz2 - 15z2

= 2y3 - 10z3 + 7yz2 - 15z2

Note:

We can also place one polynomial beneath the other and subtract like terms.

To do the subtraction, we change the sign of each term being subtracted, then add.

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