...each are positive, we have the following RULE, FOR MULTIPLYING ONE POLYNOMIAL BY ANOTHER. Multiply each term of the multiplicand by each term of the multiplier, and add the products together. 2. 3. a+ba?b+cd a+b ab+ciF a'+ab aV+abcd ab+b* a'+2ab+bi a'b'+a'bcd'+abcd+c1^...

...See §67. Hence, we have, for the multiplication of polynomials, the following RULE. § 71. Multiply each term of the multiplicand by each term of the multiplier, and add the products. See Geom. §178. Cor. III. a.) This is precisely the method employed in Arithmetic. Thus,...

...4 a4b _ 10 a362 + 2 a2*3 6 a5 — 11 a46 — 7 a362 + 2 a"63. In this operation, we have multiplied each term of the multiplicand by each term of the multiplier, and the number of partial products formed is, therefore, equal to the product of the number of terms in...

...each are positive, we have the following RULE FOE MULTIPLYING ONE POLYNOMIAL BY ANOTHER. — Multiply each term of the multiplicand by each term of the multiplier, and add the products together. EXAMPLES. 2. Multiply x-\-y by a-\-c. Ans. ax-\-ay-\-cx-\-cy. 3. Multiply 2a4-3z...

...(55.) The whole doctrine of multiplication is therefore com prehended in the following ROLE. Multiply each term of the multiplicand by each term of the multiplier, and add together all the partial products, observing '.hat like signs require + in the product, and unlike signs — EXAMPLE...

...minus. (63.) Hence all the cases of multiplication are comorehended in the following * RULE. Multiply each term of the multiplicand by each term of the multiplier, and add together all the partial products, observing that like signs require + in the product, and unlike signs —. Examples....

...Multiply each of its terms by the other factor. 20. When both factors are compound. Multiply eacli term of the multiplicand by each term of the multiplier, and add the partial products, as in Arithmetic. Multiply EXERCISES. (1.) a by Ь Ans. a6. (2.) .«e by y. .......

...we deduce the following rule : In order to effect the multiplication of two algebraic expressions, multiply successively each term of the multiplicand by each term of the multiplier ; observing, that if two terms of the multiplicand and multiplier are affected with the same sign,...

...Haxy~*c. CASE III. (91.) When both the multiplicand and multiplier are polynomials. RULE. Multiply each term of the multiplicand by each term of the multiplier, and add the products. PROBLEM. Multiply a' + 06 + 6* by a + 6. SOLUTION. Operation. a*+ a6 + 6' Multiplying...

...sum of these partial products is 2ar" -|- xy — y*, the product required. Hence, the BULB. Multiply each term of the, multiplicand by each term of the multiplier, and add the partial products. EXAMPLES. (2.) (3.) (4.) 3a-)-5a; 8a2ic — d abc -\- m" 4m bad'2 4 am 12 am...