A Treatise on Algebra: By Charles SmithMacmillan and Company, 1888 - 571 páginas |
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Página 17
... arranged in alphabetical order . 31. Since a2 = aa , and a3 = aaa ; we have a2 × a3 = aα × aaa = a = a2 + 3 So also a3 x a1 = a2 = a3 + 4 , and a1 × α = aaaa × α = a5 : 4 + 1 = In the above examples we see that the index of the product ...
... arranged in alphabetical order . 31. Since a2 = aa , and a3 = aaa ; we have a2 × a3 = aα × aaa = a = a2 + 3 So also a3 x a1 = a2 = a3 + 4 , and a1 × α = aaaa × α = a5 : 4 + 1 = In the above examples we see that the index of the product ...
Página 34
... arranged as above described : a + b a + b a- - b a2 + ab + b2 a + b a - b a2 + ab a2 + ab a3 + a2b + ab2 + ab + b2 -ab - b2 -a2b- ab2 - b3 a2 + 2ab + b2 a2 - b2 a3 -b3 a + b + c a + b + c a2 + ab + ac + ab + b2 + bc a2 + 2ab + 2ac + b2 ...
... arranged as above described : a + b a + b a- - b a2 + ab + b2 a + b a - b a2 + ab a2 + ab a3 + a2b + ab2 + ab + b2 -ab - b2 -a2b- ab2 - b3 a2 + 2ab + b2 a2 - b2 a3 -b3 a + b + c a + b + c a2 + ab + ac + ab + b2 + bc a2 + 2ab + 2ac + b2 ...
Página 35
... arranged according to descending powers of a . In like manner we say that the expression is arranged according to ascending powers of b . 59. Although it is not necessary to arrange the terms either of the multiplicand or of the ...
... arranged according to descending powers of a . In like manner we say that the expression is arranged according to ascending powers of b . 59. Although it is not necessary to arrange the terms either of the multiplicand or of the ...
Página 36
... arranged according to descending , or to ascending , powers of some letter , much of the labour of multiplication can be saved by writing down the coefficients only . Thus , to multiply 3x2 - x + 2 by 3x2 + 2x - 2 , we write 3-1 + 2 3 + ...
... arranged according to descending , or to ascending , powers of some letter , much of the labour of multiplication can be saved by writing down the coefficients only . Thus , to multiply 3x2 - x + 2 by 3x2 + 2x - 2 , we write 3-1 + 2 3 + ...
Página 40
... arrange expressions in this way . Again , to find ( x2 + a2 ) 2 ( x + α ) 2 ( x − a ) 2 . - The factors can be taken in any order ; hence the required product = [ ( x − a ) ( x + a ) ( x2 + a2 ) ] 2 = [ ( x2 − a2 ) ( x2 + a2 ) ] 2 ...
... arrange expressions in this way . Again , to find ( x2 + a2 ) 2 ( x + α ) 2 ( x − a ) 2 . - The factors can be taken in any order ; hence the required product = [ ( x − a ) ( x + a ) ( x2 + a2 ) ] 2 = [ ( x2 − a2 ) ( x2 + a2 ) ] 2 ...
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Términos y frases comunes
a+b+c a₁ arithmetic mean arithmetical progression ax² b₁ binomial Binomial Theorem C₁ Cambridge coefficient contain continued fraction Crown 8vo denominator determinant digits divergent divide divisible divisor Edition equal equation ax example expansion Extra fcap Fcap Find the number Find the sum follows geometrical progression given expression Globe 8vo greater Hence the required infinity letters logarithm MACMILLAN'S Multiply negative nth convergent nth root nth term number of terms obtained P₁ periodic continued fraction positive integer powers prime number Professor prove quadratic equation quadratic surd quotient ratio remainder School Shew Solve the equation square root subtract suppose Theorem Trinity College u₁ unknown quantities white ball whole number zero
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