New Elementary Algebra |
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a b c a² b² 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 equal Explain the operation Explain the solution Extract the square Find the greatest Find the sum find the values 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 equation quadratic form quan quotient radical sign ratio Reduce remainder Repeat the Rule Required the square second member second operation simple equations solution of Problem square root subtraction Theorem tion tity transposing unknown quantity Whence
Popular passages
Page 54 - 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 299 - ... 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 288 - ... two triangles are to each other as the products of their bases by their altitudes.
Page 170 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.
Page 71 - The LEAST COMMON MULTIPLE of two or more quantities is the least quantity that can be divided by each of them without a remainder.
Page 275 - 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 176 - 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 51 - 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 302 - The mean proportional between two quantities is equal to the square root of their product.
Page 55 - ... 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.