Algebra Tutorials! Home 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 Powers 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 = axÂ·cx = acx2 . C = bÂ·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 â€œouterâ€ and â€œinnerâ€ are placed directly below and then added algebraically along with the product of the â€œfirstsâ€ and â€œlastsâ€. 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 Â± 3)2 is called the square of a binomial or perfect square trinomial: 4x2 Â± 12x 9 Attach  Â±  sign of binomial  (always ) (2x Â± 3)(2x Â± 3) or (2x Â± 3)2 4x2 Â± 12x + 9
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