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3.3. Multiplication

Multiplying each term in the first polynomial by each term in the second polynomial and then combining similar terms gives the product of two polynomials. For example: 

(2x2 + 3x + 4)(5x + 4) = 
2x2(5x + 4) + 3x(5x + 4) + 4(5x + 4) = 
10x3 + 8x2 + 15x2 + 12x + 20x + 16 = 
10x3 + 23x2 + 32x + 16
The degree of the result is equal to the sum of the degrees of the multiplier and multiplicand.

FOIL method

The need to multiply of binomials is common in mathematics. A memory aid to help one obtain all the terms correctly is: multiply the First terms, then the Outer terms, then the Inner terms, and finally the Last terms. This is known as the FOIL method; it works as follows: 
(a + b)(c + d) = ac + ad + bc + bd
An example: 
(x + 4)(2x + 3) = 2x2 + 3x + 8x + 12 = 
2x2 + 11x + 12
Another example: 
(x + 2)(x + 3) = x2 + 5x + 6

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Copyright © 2004, Stephen R. Schmitt