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Solving Quadratic Equations by Completing the Square
Graphing Logarithmic Functions
Division Property of Exponents
Adding and Subtracting Rational Expressions With Like Denominators
Rationalizing the Denominator
Multiplying Special Polynomials
Functions
Solving Linear Systems of Equations by Elimination
Solving Systems of Equation by Substitution and Elimination
Polynomial Equations
Solving Linear Systems of Equations by Graphing
Quadratic Functions
Solving Proportions
Parallel and Perpendicular Lines
Simplifying Square Roots
Simplifying Fractions
Adding and Subtracting Fractions
Adding and Subtracting Fractions
Solving Linear Equations
Inequalities in one Variable
Recognizing Polynomial Equations from their Graphs
Scientific Notation
Factoring a Sum or Difference of Two Cubes
Solving Nonlinear Equations by Substitution
Solving Systems of Linear Inequalities
Arithmetics with Decimals
Finding the Equation of an Inverse Function
Plotting Points in the Coordinate Plane
The Product of the Roots of a Quadratic
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Solving Quadratic Equations by Completing the Square
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Multiplying Special Polynomials

Multiplying Polynomials, Special Cases:

Review general products FOIL Multiplying Polynomials:
What to Do How to Do It
1. Look again at the product of two binomials, and see how we use the method called the double distributive property. (A + B)(C + D)

 = A(C + D) + B(C + D)

= AC + AD + BC + BD

2. Generally, product of two linear binomials is multiplied by the method called F O Ι L.  to obtain a quadratic (2nd degree) trinomial:

F = the product of the first terms:

O = the product of the outer terms:

Ι = the product of the inner terms

L = the product of the last terms

Algebraically add the O + Ι = adx + bcx = Bx.

 (Keep these steps in mind for reversing later.)

 (ax + b)(cx + d)

Ax2 + Bx + C

Ax2 = ax·cx = acx2 .

C = b·d = bd

acx2 + (ad +bc)x + bd

= Ax2 + Bx + C

3. For general linear (first degree) binomials with common terms: 

The double distributive property is used vertically - the “outer” and “inner” are placed directly below and then added algebraically along with the product of the “firsts” and “lasts”.

The algebraic sum is the Product:

(ax + b)(cx + d)

4. A special case occurs when the two factors are the same. [Beginners should always FOIL it.]

(2x ± 3)2 is called the square of a binomial

or

perfect square trinomial: 4x2 ± 12x 9

Attach  ±  sign of binomial  (always )

(2x ± 3)(2x ± 3) or (2x ± 3)2

4x2 ± 12x + 9

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