Algebra Tutorials!  
     
     
Tuesday 23rd of December
   
Home
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
Mixed
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Algebra
Order of Operations
Dividing Complex Numbers
Polynomials
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Factoring
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Numbers
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Fractions
Polynomials
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Exponents
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Radicals
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
   

The Square of a Binomial

To compute (a + b)2, the square of a binomial, we can write it as (a + b)(a + b) and use FOIL:

(a + b)2 = (a + b)(a + b)
  = a2 + ab + ab + b2
  = a2 + 2ab + b2

So to square a + b, we square the first term (a2), add twice the product of the two terms (2ab), then add the square of the last term (b2). The square of a binomial occurs so frequently that it is helpful to learn this new rule to find it. The rule for squaring a sum is given symbolically as follows.

 

The Square of a Sum

(a + b)2 = a2 + 2ab + b2

 

Example 1

Using the rule for squaring a sum

Find the square of each sum.

a) (x + 3)2

b) (2a + 5)2

Solution

a) (x + 3)2 = x2 +  2(x)(3) + 32

= x2 + 6x + 9

   
  Square of first Twice the procuct Square of last  
b) (2a + 5)2 = (2a)2 + 2(2a)(5) + 52
  = 4a2 + 20a + 25

Caution

Do not forget the middle term when squaring a sum. The equation (x + 3)2 = x2 + 6x + 9 is an identity, but (x + 3)2 = x2 + 9 is not an identity. For example, if x = 1 in (x + 3)2 = x2 + 9, then we get 42 = 12 + 9, which is false.

When we use FOIL to find (a - b)2, we see that

(a - b)2 = (a - b)(a - b)
  = a2 - ab - ab + b2
  = a2 - 2ab + b2

So to square a - b, we square the first term (a2), subtract twice the product of the two terms (-2ab), and add the square of the last term (b2). The rule for squaring a difference is given symbolically as follows.

 

The Square of a Difference

(a - b)2 = a2 - 2ab + b2

 

Example 2

Using the rule for squaring a difference

Find the square of each difference.

a) (x - 4)2

b) (4b - 5y)2

Solution

a) (x - 4)2 = x2 - 2(x)(4) + 42
  = x2 - 8x + 16
b) (4b - 5y)2 = (4b)2 - 2(4b)(5y) + (5y)2
  = 16b2 - 40by + 25y2
 
Copyrights © 2005-2014