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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)

→ 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€.