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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 = 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