First Lessons in Algebra: Embracing the Elements of the ScienceWiley & Putnam, 1839 - 252 sider |
Inni boken
Resultat 1-5 av 33
Side 12
... results from multiplying the quantity by itself . Thus , in the example a3 = 43-4x4x4 = 64 , 64 is the third power of 4 , and the exponent 3 shows the degree of the power . 15. The sign , is called the radical sign , and when QUEST ...
... results from multiplying the quantity by itself . Thus , in the example a3 = 43-4x4x4 = 64 , 64 is the third power of 4 , and the exponent 3 shows the degree of the power . 15. The sign , is called the radical sign , and when QUEST ...
Side 18
... result the sign of the greater . REMARK . - It should be observed that the reduction affects only coefficients , and not the exponents . EXAMPLES . 1. Reduce to its simplest form the polynomial + 2a3bc2 - 4a3bc2 + 6a3bc2 — 8a3bc2 + ...
... result the sign of the greater . REMARK . - It should be observed that the reduction affects only coefficients , and not the exponents . EXAMPLES . 1. Reduce to its simplest form the polynomial + 2a3bc2 - 4a3bc2 + 6a3bc2 — 8a3bc2 + ...
Side 19
... result is . 3a + 5b + 2c an expression which cannot be reduced to a more simple form . QUEST . - 26 . What is addition in Algebra ? What is such simplest and equivalent expression called ? 4a2b3 Again , add together the monomials 2a2b3 ...
... result is . 3a + 5b + 2c an expression which cannot be reduced to a more simple form . QUEST . - 26 . What is addition in Algebra ? What is such simplest and equivalent expression called ? 4a2b3 Again , add together the monomials 2a2b3 ...
Side 20
... result after reducing ( Art . 25 ) , is .. 13a2b3 3. Let it be required to find the sum of the expressions 2a2-4ab 3a2-3ab + b2 2ab - 5b2 Their sum , after reducing ( Art . 25 ) is . 5a2 - 5ab - 4b2 27. As a course of reasoning similar ...
... result after reducing ( Art . 25 ) , is .. 13a2b3 3. Let it be required to find the sum of the expressions 2a2-4ab 3a2-3ab + b2 2ab - 5b2 Their sum , after reducing ( Art . 25 ) is . 5a2 - 5ab - 4b2 27. As a course of reasoning similar ...
Side 25
... result to its simplest form . ( 1 ) EXAMPLES . From 6ac - 5ab + c2 Take Rem . 3ac + 3ab + 7c 3ac - 8abc2 - 7c . ( 2 ) From 6ax - a + 362 Take 9ax + x + b2 Rem . From -3ax - a + x + 2b2 . ( 4 ) 5a3-4a3b + 362c Take -2a3 + 3a2b- 8b2c Rem ...
... result to its simplest form . ( 1 ) EXAMPLES . From 6ac - 5ab + c2 Take Rem . 3ac + 3ab + 7c 3ac - 8abc2 - 7c . ( 2 ) From 6ax - a + 362 Take 9ax + x + b2 Rem . From -3ax - a + x + 2b2 . ( 4 ) 5a3-4a3b + 362c Take -2a3 + 3a2b- 8b2c Rem ...
Andre utgaver - Vis alle
First Lessons in Algebra: Embracing the Elements of the Science Charles Davies Uten tilgangsbegrensning - 1840 |
First Lessons in Algebra: Embracing the Elements of the Science Charles Davies Uten tilgangsbegrensning - 1839 |
First Lessons in Algebra: Embracing the Elements of the Science Charles Davies Uten tilgangsbegrensning - 1841 |
Vanlige uttrykk og setninger
algebraic quantities arithmetical means arithmetical progression binomial Binomial Theorem called cents common denominator common difference complete equation completing the square composed contain contrary sign cube decimal denotes Divide dividend division divisor dollars double product enunciation equation involving EXAMPLES exponent extracting the square fifth power figure find a number Find the square Find the sum Find the values following RULE four quantities fourth power geometrical progression Give the rule given number greater greyhound Hence last term least common multiple minus mixed quantity monomial Multiply negative number expressed number of terms obtain ounces of silver perfect square polynomial question quotient radical sign ratio Reduce remainder second degree second power second term simplest form square root Substituting this value take the equation tens third three terms tion transposing trinomial twice the product unknown quantity values of x Verification whence yards
Populære avsnitt
Side 230 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A ; B ; : C : D; and read, A is to B as C to D.
Side 231 - Quantities are said to be in proportion by composition, when the sum of the antecedent and consequent is compared either with antecedent or consequent.
Side 155 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.
Side 233 - AC and by clearing the equation of fractions we have BO=AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means.
Side 175 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Side 138 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend But if any of the products should be greater than the dividend, diminish the last figure of the root.
Side 214 - A merchant bought cloth for which he paid £33 15s., which he sold again at £2 8s. per piece, and gained by the bargain as much as one piece cost him : how many pieces did he buy ? Ans.
Side 35 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.
Side 214 - To find a number such that if you subtract it from 10, and multiply the remainder by the number itself, the product shall be 21. Ans. 7 or 3.
Side 230 - Of four proportional quantities, the first and third are called the antecedents, and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order...