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Multiplying Polynomials

Multiplying Polynomials

Examples

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.

  (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)

   


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