An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 6
... obtained . When these sums are equal they cancel each other , and the corresponding terms are to be omitted . a2 Thus , a2b - 9 ab2 +8 a2b + 5c - 3 a2 b + 8 a b2 + 2 a2b + c + a b2 - 8 c is the same as 8 a2 b — 2 c . 21 . EXAMPLES . 1 ...
... obtained . When these sums are equal they cancel each other , and the corresponding terms are to be omitted . a2 Thus , a2b - 9 ab2 +8 a2b + 5c - 3 a2 b + 8 a b2 + 2 a2b + c + a b2 - 8 c is the same as 8 a2 b — 2 c . 21 . EXAMPLES . 1 ...
Page 7
... obtained can be reduced to its simplest form by art . 20 . 24. EXAMPLES . Ans . 2 x . 1. Find the sum of a and a . Ans . 2 a . 2. Find the sum of 11 x and 9 x . Ans . 20 x . 3. Find the sum of 11 x and 9x . 4. Find the sum of 11 x and 9 ...
... obtained can be reduced to its simplest form by art . 20 . 24. EXAMPLES . Ans . 2 x . 1. Find the sum of a and a . Ans . 2 a . 2. Find the sum of 11 x and 9 x . Ans . 20 x . 3. Find the sum of 11 x and 9x . 4. Find the sum of 11 x and 9 ...
Page 8
... obtained by increasing C - A by the excess of A above A - B , that is , by B , and it is thus found to be C- A + B. The same result would be obtained by adding to C the quantity AB , with its signs reversed , so as to make it -A + B ...
... obtained by increasing C - A by the excess of A above A - B , that is , by B , and it is thus found to be C- A + B. The same result would be obtained by adding to C the quantity AB , with its signs reversed , so as to make it -A + B ...
Page 11
... obtained from the product of the negative term of one factor by the positive term of the other , as -C by B or -D by A. Hence , The product of two polynomials is obtained by multiplying each term of one factor by each term of the other ...
... obtained from the product of the negative term of one factor by the positive term of the other , as -C by B or -D by A. Hence , The product of two polynomials is obtained by multiplying each term of one factor by each term of the other ...
Page 13
... obtained ; and , therefore , by art . 15 , the degree of each term of the product is equal to the sum of the degrees of the factors . Thus , in example 16 , the degree of each factor is 12 , and that of the product is 12 + 12 or 24 . 2 ...
... obtained ; and , therefore , by art . 15 , the degree of each term of the product is equal to the sum of the degrees of the factors . Thus , in example 16 , the degree of each factor is 12 , and that of the product is 12 + 12 or 24 . 2 ...
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126 become zero 3d root arithmetical progression coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence