Manual of AlgebraBarnes, 1875 - 331 páginas |
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Página 20
... hence , in this case , the sum of the monomials is + 16a2bc . In the second example the same unit is taken negatively 8 times , 1 time , 3 times , and 2 times , that is , it is taken negatively 14 times ; hence , the sum of the ...
... hence , in this case , the sum of the monomials is + 16a2bc . In the second example the same unit is taken negatively 8 times , 1 time , 3 times , and 2 times , that is , it is taken negatively 14 times ; hence , the sum of the ...
Página 21
... hence , we have the following rule for the addition of polynomials : RULE . I. Write the quantities to be added so that sim- ilar terms shall fall in the same column . II . Add each column of similar terms sepa- rately , and to the ...
... hence , we have the following rule for the addition of polynomials : RULE . I. Write the quantities to be added so that sim- ilar terms shall fall in the same column . II . Add each column of similar terms sepa- rately , and to the ...
Página 30
... Hence , we have the following rule for signs : RULE . If two factors have like signs , their product is + , if they have unlike signs , their product is Operation of Multiplication . - . 28. In algebraic multiplication , there may be ...
... Hence , we have the following rule for signs : RULE . If two factors have like signs , their product is + , if they have unlike signs , their product is Operation of Multiplication . - . 28. In algebraic multiplication , there may be ...
Página 31
... hence , 3a2bc4a3b2c4 — 12a5b3c5 . In like manner we may find the product of any two monomials ; hence , the following rule for the multipli- cation of monomials : RULE . Multiply the coefficients together for a new co- efficient ; after ...
... hence , 3a2bc4a3b2c4 — 12a5b3c5 . In like manner we may find the product of any two monomials ; hence , the following rule for the multipli- cation of monomials : RULE . Multiply the coefficients together for a new co- efficient ; after ...
Página 32
... hence , the required product is 168ab3cx2 , Ans . - 13. Find the continued product of 3pqr , - 2p2qr3 , and 4prix . Ans . 24pq28x . 14. Find the continued product of and 5mnd . Ans . -- - 3m3d , 4md2 , 60m2 + 2nd1 . 6 15. Find the ...
... hence , the required product is 168ab3cx2 , Ans . - 13. Find the continued product of 3pqr , - 2p2qr3 , and 4prix . Ans . 24pq28x . 14. Find the continued product of and 5mnd . Ans . -- - 3m3d , 4md2 , 60m2 + 2nd1 . 6 15. Find the ...
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Términos y frases comunes
algebraic Arithmetic ax² binomial formula called clearing of fractions coefficients common difference contain contrary signs cube root Davies denominator denote the number distance dividend divisible equa equal roots equation whose roots EXAMPLES exponent expression extracting the square factors Find the cube Find the greatest Find the least Find the square Find the sum following principle following rule geometrical geometrical progression given equation greatest common divisor hence imaginary indicated irreducible fraction least common multiple logarithm Mathematics miles minuend monomial multiplying both members negative nth root number of terms operation partial fractions polynomial positive preceding problem proportion quan quotient radical sign ratio real roots Reduce remainder resulting equation roots equal second degree second member second term solved square root Sturm's Theorem substituting subtract third tion tity transposing travels unknown quantity V₁ whole number
Pasajes populares
Página 145 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Página 239 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Página 267 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 245 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.
Página 42 - ... the first term of the quotient ; multiply the divisor by this term and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...
Página 239 - In any proportion, the product of the means is equal to the product of the extremes.
Página 245 - That is, any term is equal to the first term, plus the product of the common difference by the number of preceding terms.
Página 41 - 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.
Página 264 - THE LOGARITHM: of a number is the exponent of the power to which it is necessary to raise a fixed number, to produce the given number. The fixed number is called the base of the system.