Manual of AlgebraBarnes, 1875 - 331 páginas |
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Página 14
... mean a numerical coefficient . If no coefficient is written , the coefficient 1 is always understood . 8. An algebraic expression is an expression for a quantity written in algebraic language , that is , by means of algebraic symbols ...
... mean a numerical coefficient . If no coefficient is written , the coefficient 1 is always understood . 8. An algebraic expression is an expression for a quantity written in algebraic language , that is , by means of algebraic symbols ...
Página 49
... means of prin- ciple 1 ° , Art . 35 . 8. Factor a2 + 2ab + b2 . 9. Factor 4x2 + 12xy + 9y2 . 10. Factor x2 + 12x + 36 . 11. Factor 4x4 + 4x2y + y2 . Ans . ( a + b ) ( a + b ) . Ans . ( 2x + 3y ) ( 2x + 3y ) . Ans . ( x + 6 ) ( x + 6 ) ...
... means of prin- ciple 1 ° , Art . 35 . 8. Factor a2 + 2ab + b2 . 9. Factor 4x2 + 12xy + 9y2 . 10. Factor x2 + 12x + 36 . 11. Factor 4x4 + 4x2y + y2 . Ans . ( a + b ) ( a + b ) . Ans . ( 2x + 3y ) ( 2x + 3y ) . Ans . ( x + 6 ) ( x + 6 ) ...
Página 50
... means of principle 3 ° , Art . 35 . 21. Factor a2 - b2 . 22. Factor 4x2 9y2 . - 23. Factor a2c2 - b2d2 . ― 24. Factor 9a2x2 - 16a2y2 . 25. Factor 25a4b4x4 26. Factor 4924 - - Ans . ( a + b ) ( a — b ) . Ans . ( 2x + 3y ) ( 2x — 3y ) ...
... means of principle 3 ° , Art . 35 . 21. Factor a2 - b2 . 22. Factor 4x2 9y2 . - 23. Factor a2c2 - b2d2 . ― 24. Factor 9a2x2 - 16a2y2 . 25. Factor 25a4b4x4 26. Factor 4924 - - Ans . ( a + b ) ( a — b ) . Ans . ( 2x + 3y ) ( 2x — 3y ) ...
Página 55
... means of the following ad- ditional principles : 2 ° . The monomial factors common to each polynomial may be suppressed ; if , however , any factor so sup- pressed is common to the two , it must be set aside as a factor of the greatest ...
... means of the following ad- ditional principles : 2 ° . The monomial factors common to each polynomial may be suppressed ; if , however , any factor so sup- pressed is common to the two , it must be set aside as a factor of the greatest ...
Página 60
... means of the greatest common divisor . Method by Factoring . 51. To deduce a rule for finding the least common multiple by the method by factoring , let it be required to find the least common multiple of 12ax , 27axs , and 30axy ...
... means of the greatest common divisor . Method by Factoring . 51. To deduce a rule for finding the least common multiple by the method by factoring , let it be required to find the least common multiple of 12ax , 27axs , and 30axy ...
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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.