...7. CASE III. When both multiplier and multiplicand are compound quantities. RULE. 38. Multiply every term of the multiplicand by each term of the multiplier, and add the several products thus obtained. It is obvious from the note to page 22, and from Art. 11, that...

...times ....... ad-\-brl-\-cd taken/times ........ -\-af-\-bf-\-cf entire product .... ad+bd+cd+af+bf+cf. Therefore, in order to multiply together two polynomials...the multiplier, and add together all the products. EXAMPLES. 1. Multiply ..... 3a2+ by ..... , 2o +56 The product, after reducing, +15a26+20a becomes...

...taken d times, .... ad+bd+cd taken /times . . . __ +af+bf+cf entire product . . ad+bd+cd+af+bf+cf. Therefore, in order to multiply together two polynomials...the multiplier, and add together all the products. Multiply by . . 3a3i . 2ia3 . (4) , . 12a3* . , . 12a;3y . (5) , . &xyz . ay*z (6) If the terms are...

.......... ad+bH+ed taken/times ........ ^-af+lf+cf entire product .... ad-\-bd-\-cd-l[-af-\-t>f-\-cf. Therefore, in order to multiply together two polynomials...additive terms : Multiply successively each term of tlic multiplicand by each term of the multiplier, and add together all the products. EXAMPLrls. 1....

...d times ....... ad+bd+cd taken /times ..... . . . +af+bf+cf entire product .... ad+bd+cd+af+bf+cf. Therefore, in order to multiply together two polynomials...the multiplier, and add together all the products. EXAMPLES. 1. Multiply ..... 3a2+ 4a6+62 by ...... 2a + 5b _ 6a3+ 8cPb+2abz The product, after reducing,...

...sign minus: (55.) The following rule then comprehends the whole doctrine of multiplication. 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 — . EXAMPLE...

...sign minus: (55.) The following rule then comprehends the whole doctrine of multiplication. Multiply each term of the multiplicand, by each term of the multiplier, and add together all tht partial products, observing that like signs require + in the product, and unlike signs — . EXAMPLE...

...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...