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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)

Ax^{2} + Bx + C

Ax^{2} = axÂ·cx = acx^{2} .

C = bÂ·d = bd

acx^{2} + (ad +bc)x + bd

= Ax^{2} + 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.]