CASE I. When the factors are both simple quantities. RULE. Multiply the coefficients of the two terms together, and to the product annex all the letters, or their powers, belonging to each, after the manner of a word ; and the result, with the proper sign prefixed, will be the product required (d). (d) When any number of quantities are to be multiplied toge. ther, it is the same thing in whatever order they are placed: thus, if ab is to be multiplied by c, the product is either abc, acl, or bras. CASE II. When one of the factors is a.compound quantity. RULE. Multiply every term of the compound factor, considered as a multiplicand, separately, by the multiplier, as in the forney case ; then' these products, placed one after another, with their proper sighs, wil be the whole product required. &c. ; though it is usual, in this case, as well as in addition and subtraction, to put them according to their rank in the alphabet. It may here also be observed, in conformity to the rule given abve for the signs, that (+a)x(+0), or (-a)X(-6) – to ab; and (ta) x (-6), or (-a)x(+b) = ab. CASE III. When both the factors are compound quantities. RULE. Multiply every term of the multiplicand separately, by each term of the multiplier, setting down the products one after another, with their proper signs ; then add the several lines of products together, and their will be the whole product required. organa senhora EXAMPLES 1. Required the product of 23 - xy+ja and x-toy. 2. Required the product of 23-4ay+wy tyand LY: 3. Required the product of x2 + xy+y? and ? xy+ya. 4. Required the product of 3x2 - 2xy+5 and x2 + 2xy -3. 5. Required the product of 2a2 – 3ax +-4x2 and 542 6ax - 2x2. 6. Required the product of 5x3+4x2+3a2xtas, and 2x2 – 3axta2. 7. Required the product of 3x3 +2x"ya +3y3 and 2x3 3x2y +5y3. 8. Regiced the product of ** -ax-+-6x - c. and de. DIVISION. Division is the converse of multiplication, and is performed like that of numbers; the male being usually divided into three cases ; in each of which like signs give t in the quotient, and unlike signs as. in finding their pöğducts (e). It it were also to be observed, that powers and roots of the same quantity, are divided by subtracting the index of the divisor from that of the dividend. Thus, dea?, or as a 2 - ab ke) According to the rule here given for the signs, it follows that tab mab tab eta, =ta, -a, ob, -b as will readily appear by multiplying the quotient by the divisor ; the signs of the products being then the same as would take place in the former rule. -b CASE I. When the divisor and dividend are both simple quantities. RULE. Set the dividend over the divisor, in the manner of a fraction, and reduce it to its simplest form, by cancelling the letters and figures that are common to each term. a a 2a Also – 2a = 3a, or = - }; and 9x13x1=3x+ За 1. Divide 16x? by 8x, and 12ax2 by 2. Divide 15aya by 3ay, and - 18ax'y by- Sax. Divide-a? -žał by za7, and axłbyatch. CASE II. When the divisor is a simple quantity, and the dividend a compound one'. RULE. Divide each term of the dividend by the divisor, as in the former case ; setting down such as will not divide ia the simplest form they will admit of. |