Algebra Tutorials!
Wednesday 18th of January
Solving Linear Equations
Systems of Linear Equations
Solving Linear Equations Graphically
Algebra Expressions
Evaluating Expressions and Solving Equations
Fraction rules
Factoring Quadratic Trinomials
Multiplying and Dividing Fractions
Dividing Decimals by Whole Numbers
Adding and Subtracting Radicals
Subtracting Fractions
Factoring Polynomials by Grouping
Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
Solving Quadratic Equations
Simplifying Complex Fractions
Common Logs
Operations on Signed Numbers
Multiplying Fractions in General
Dividing Polynomials
Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
Solving Linear Equations
The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
Straight Lines
Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
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Using Patterns to Multiply Two Binomials

We can use FOIL to find the product of any two binomials. Sometimes we can find certain binomial products more quickly by recognizing patterns.

For example, let’s first use FOIL to find (a + b)2.

Use the definition of exponential notation to write (a + b)2 as the product of two binomials. (a + b)2 = (a + b)(a + b)

Combine like terms.

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

  = a2 + ab + ba + b2

= a2 + 2ab + b2


Note that (a + b)2 is not equal to a2 + b2. Don’t forget the middle term, 2ab.


We obtain a similar pattern when we square a binomial that is a difference rather than a sum.


Formula — Square of a Binomial

Let a and b represent any real numbers.

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

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


When a binomial is squared, the resulting trinomial is called a perfect square trinomial.

For example, both a2 + 2ab + b2 and a2 - 2ab + b2 are perfect square trinomials.



When we refer to integers, a perfect square is an integer that is the square of another integer:

9 is a perfect square because it is the result of squaring 3.

A similar situation exists for variables:

a2 is a perfect square because it is the result of squaring a.

64n2 is a perfect square because it is the result of squaring 8n.


Example 1

Find: (6y2 + 5)2


The expression (6y2 + 5)2 is in the form (a + b)2.

So, we can use the formula for the square of a binomial.

(a + b)2

= a2 + 2ab + b2
Substitute 6y2 for a and 5 for b.


So, (6y2 + 5)2 = 36y4 + 60y2 + 25

(6y2 + 5)2


= (6y2)2 + 2(6y2)5 + (5)2

= 36y4 + 60y2 + 25

Note that (6y2 + 5)2 (6y2)2 + (5)2. Don’t forget the middle term, 60y2.


Example 2

Find: (3w - 7y)(3w - 7y)


Since (3w - 7y)(3w - 7y) = (3w - 7y)2, we can use the shortcut for the square of a binomial.

(a - b)2

= a2 - 2ab + b2
Substitute 3w for aand 7y for b.


(3w - 7y)2


= (3w)2 + 2(3w)(7y) + (7y)2

= 90w2 - 42wy + 49y2

So, (3w - 7y)(3w - 7y) = 90w2 - 42wy + 49y2.
Note that (3w2 - 7y)2 (3w2)2 - (7y)2. Don’t forget the middle term, -42wy2.
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