MULTIPLICATION. ZSj 



CASE III. 



U^hen both the factors arc coinpouud quantities. 



RULE. 



Multiply each term of the multiplicand by each term of 

 the multiplier ; then add all the products together, and the 

 sum will be the product required. "^ 



* In the first example, we multiply a-^-h, the multiplicand, into 

 ^7, the first term of the multiplier, and the product is a'^ J^ah ; 

 then we multiply the multiplicand into ^, the second term of the 

 multiplier, and the product is ah^^b'^. The sum of tlicse two 

 products is dE* + 2«3-f-3*, as above, and is the square of a-\-h. 

 In the first example, the like terms of the product, viz. ah 

 and aby together make zab j but in the second, example, the 

 terms -\-ab and -^ah^ having contrary signs, destroy each 

 Other, and the product is <«^' — b"^ , the difFerence of the squares 

 of ^ and 3. Hence it appears,, that the sura and difference o^ 

 two quantities, multiplied together, produce the diiference oi 

 their squares. And by the next following example you mav ob. 

 ser^, that the square of the difference of two quantities, as ci 

 and^j is equal to a* — 2a^-|-i^, the sum of their sq\?arer. mimiT* 

 twice their product. 



