New Elementary Algebra: In which the First Principles of Analysis are Progressively Developed and Simplified : for Common Schools and Academies |
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a² b² affected quadratic equation algebraic quantities arithmetical mean binomial factors cents Clearing of fractions coefficient common denominator common difference complete the square cube root Define degree denote Divide dividend division entire quantity equa Explain the operation Explain the solution Extract the square Find the greatest Find the sum find the values formulas fractional exponent geometrical progression Given x² greatest common divisor indicated last term least common multiple letter lowest terms miles monomial Multiply negative exponents NOTE number of terms obtain perfect square polynomial positive proportion quadratic form quan quotient radical sign ratio Reduce remainder Repeat the Rule required the number Required the square second member second power simple equations solution of Problem square root subtraction Theorem tion tity transposing unknown quantity Whence
Popular passages
Page 56 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 289 - ... that is, Any term of a geometric series is equal to the product of the first term, by the ratio raised to a power, whose exponent is one less than the number of terms. EXAMPLES. 1.
Page 53 - 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 168 - Hence, for raising a monomial to any power, we have the following RULE. Raise the numerical coefficient to the required power, and multiply the exponent of each letter by the exponent of the required power.
Page 279 - Divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5. Ans. 20 and 40.
Page 57 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 182 - 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.
Page 92 - SUBTRACTION OF FRACTIONS is the process of finding the difference between two fractions.
Page 55 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 192 - RULE. Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.