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Note. When the quantities that are to be multiplied together
efficients of the resulting terms, between brackets, as in the former rule. And if several compound quantities are to be multiplied together, multiply the first by the second, and then that product by the third, and so on to the last factor, as below.
To this we may add, that it is usual, in some cases, to write down the quantities that are to be multiplied, together, between brackets, or under a vinculum, without performing the whole operation; as 3ab(a+b)xaa/(a”—b")
41. Division in Algebra is the method of finding the quotient arising from the division of one algebraic quantity by another. Division is generally divided into three cases, namely, when the divisor and dividend are both simple quantities; when the divisor is a simple quantity and the dividend a compound one; and when the divisor and dividend are both compound quantities. CASE I. When the divisor and dividend are both simple terms. RULE. Place the divisor in the form of a denominator under the dividend; cancel those letters which are common to both, and divide the coefficients by any number that will divide them without a remainder, and the result will be the quotient required. RULE II. Divide the coefficients as in common arithmetic, and to the quotient annex those letters in the dividend which are not found in the divisor. A general rule for the signs in all the cases of division : When the signs of the divisor and dividend are alike, (that is, both + or both — ,) the sign of the quotient will be +. When they are unlike, (that is, the one + and the other —,) the sign of the quotient will be —. The above rule briefly expressed in one view, is as follows: Div'r. Div'd. Quo’t. Divor. Div'd. Quo’t.
and these four are all the cases that can possibly happen with regard to the variation of the signs.
Powers and roots of the same quantity are divided by subtracting their idices, that is, subtract the index of the divisor from the index of the dividend.