The Elements of Algebra |
From inside the book
Results 1-5 of 15
Page 7
... compound expressions . Simple terms are those when one letter or one combination of letters only is used , such are 5a , 76 , 8ab , 9abc , 12ab2 . Compound expressions are those when two or a greater number of simple terms are connected ...
... compound expressions . Simple terms are those when one letter or one combination of letters only is used , such are 5a , 76 , 8ab , 9abc , 12ab2 . Compound expressions are those when two or a greater number of simple terms are connected ...
Page 8
... compound under each other , and add or subtract the coefficients of like terms as in the addition of numbers , thus , 5 a 7a a + b + 3c 3 a 2a + 2b + c 8 a2 - 9x2 + 5 7 a2 + 4x2 - 3 a 3a + b + 2c 16 a 6a + 4b + 6c -11a2 + 3x2 + 13 4a2 ...
... compound under each other , and add or subtract the coefficients of like terms as in the addition of numbers , thus , 5 a 7a a + b + 3c 3 a 2a + 2b + c 8 a2 - 9x2 + 5 7 a2 + 4x2 - 3 a 3a + b + 2c 16 a 6a + 4b + 6c -11a2 + 3x2 + 13 4a2 ...
Page 17
... compound quantity , we might multiply the multipli- cand by each term of the multiplier separately , and then add together the products so obtained , for the complete re- sult ; but this would entail upon us the trouble of writing the ...
... compound quantity , we might multiply the multipli- cand by each term of the multiplier separately , and then add together the products so obtained , for the complete re- sult ; but this would entail upon us the trouble of writing the ...
Page 19
... compound , 2a2 3ab + 2b2 За - a5 - 5ab15a2b2 - 30 ab * - 2 a 6a3 - 9a3b + 6ab2 2a + 10a5b – 30 a3 b2 + 60 a2 b * -- Lastly let both multiplier and multiplicand be com- pound . a + b a + b a2 + ab + ab + b2 a - 2b 26 a - a2 - 2ab - 2ab + ...
... compound , 2a2 3ab + 2b2 За - a5 - 5ab15a2b2 - 30 ab * - 2 a 6a3 - 9a3b + 6ab2 2a + 10a5b – 30 a3 b2 + 60 a2 b * -- Lastly let both multiplier and multiplicand be com- pound . a + b a + b a2 + ab + ab + b2 a - 2b 26 a - a2 - 2ab - 2ab + ...
Page 22
... compound quantity and the divisor a simple term , the quotient is found by dividing every term of the dividend by the divisor , as in the fol- lowing examples . 5a ) 25a2 - 15ab 5a - 3b 4b ) 12a b - 1663 3a2 - 462 -2ab ) 8a2b3 - 14abc ...
... compound quantity and the divisor a simple term , the quotient is found by dividing every term of the dividend by the divisor , as in the fol- lowing examples . 5a ) 25a2 - 15ab 5a - 3b 4b ) 12a b - 1663 3a2 - 462 -2ab ) 8a2b3 - 14abc ...
Other editions - View all
Common terms and phrases
2ab+b² a²+2ab+b² a²x² a³b ab² ab³ algebraical quantities arithmetic mean arithmetic series arithmetical progression ax² binomial coefficient common difference compound cube root decimal denominator digits divided dividend division divisor equal examples expressed Extract the square factor Find the greatest find the numbers Find the sum fraction geometrical progression greatest common divisor greatest common measure Hence last term least common multiple less letters logarithm multiplied negative number of terms numbers in arithmetical P₁ permutations QUADRATIC EQUATIONS quotient ratio remainder result rule shew square root subtract surd third unity unknown quantity whence write written xy³
Popular passages
Page 38 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 199 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 22 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 173 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.