I' Multiplication of Algebra. RU L E. F the Multiplicator and Multiplicand have Signs both alike, that is both affirmative, or both negative, the Product will then be affirmative. But if one be affirmative and the other negative, then the Product will be negative. Multiplication of fimple Algebraick Quantities, is performed, firft, by multiplying all the numeral Coefficients together, and then putting down after the Product, the Letters in both Factors, the Sign of the Product being prefixed to it. The Multiplication of compound Algebraick Quantities, is performed by multiplying every particular Member of the Multiplicator into all thofe of the Multiplicand, and then reducing the whole into the leaft Compass poffible. 3+4+56 12xx-23ax+10aa+14xb—21ab10bb Divifion of Algebra S only the Reverfe of Multiplication, and all the Operations in this Rule may eafily be performed, by confidering that the Quotient multiplied by the Divifor gives the Dividend. Rule ift. If the Quantities have like Signs, but no Coefficients, expunge the Quantities in the Dividend that are in the Divifor, and put the Sign + before the Quotient, Rule 2d. If Quantities have Coefficients, divide them as in common Arithmetick, and expunge the Quantities as before. Rule 3d. If the Divifor and Dividend be the fame, the Quotient is one. Rule 4th. If the Quantities in the Divifor are not like them in the Dividend, put them down as you do a vulgar Fraction. EXAMPLES. Divide xmry by ur; place it thus xmy nr Divide 5x+4y by 5n+r; it will ftand thus 574 5.nfr If the Learner accuftom himself to afk these three Questions, it will make Division easy. First, what Sign x into the Divifor, will give the Sign prefixed to to the Dividend; fecondly, what numeral Coefficient of the Quotient, X into the numeral Coefficient of the Divifor will make that of the Dividend; and thirdly, what Letters x into those of the Divifor, will make those of the Dividend? The Signs, Coefficients, and Letters, which arife upon afking these Questions, will be the true Quotient fought, as well in compound as fimple Algebraick Quantities. EXAMPLES. -3a)12ab-4b 12ab -6xy)—24yxxx(+4xx --24YXXX 2y+3x)16yyyy-72xxyy+81xxxx(8yyy-12xy-18xxy INVOLUTION S the Multiplication of like Quantities, or the raifing of any given Quantity to any defired This axa-aa, or a2, is a Square. And aaxa aaa, or a3, is a Cube. xxxxx=xxxx, or x4, is Biquadrate of x; or the fourth Power of x, &c. x+y This is called a Binomial Root. 2x+y 1 2 15 xx+2xy+yy The Square of x+y. I 3 xxy+2xyy+yyy [8]xxx+3xxy+3xyyyyy. The Cube of x+y. |