 ... 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.  The Elements of Algebra - Σελίδα 76των Elias Loomis - 1856 - 268 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Joseph Ray - 1852 - 408 σελίδες
...j02=4z2— 4ijr+y2. 3. (3x—5zy=9xi— 30xz+25z2. 4. (02— 3cx)2=o2z2— 6 ART. 8O. THEOREM III. — The product of the sum and difference of two quantities, is equal to the difference of tlieir squares. Let a represent one of the quantities, and 6 the other ; then o-|-i=their sum, and... | |
 | James William M'Gauley - 1854 - 284 σελίδες
...+6 By a— b -ab—b2 Product a2— 62 The following formula is obtained from this example : — " the product of the sum and difference of two quantities, is equal to the difference of their squares." And, for the reason just given [35] it, also, is general. 37. EXAMPLE 3. — Multiply c — d By c... | |
 | Elias Loomis - 1855 - 356 σελίδες
...5— x/3 Product, 25-3=22, as required. These two examples are comprehended under the Rule in Art. 62, the product of the sum and difference of two quantities is equal to the difference of their squares. Ex. 3. Find a multiplier that shall make v/5+v/3 rational and determine the product. Ex. 4. Find a... | |
 | Charles Davies, William Guy Peck - 1855 - 628 σελίδες
...number of factors. The following are some of the properties of products with respect to their forms : 1. The product of the sum and difference of two quantities is equal to the difference of their squares ; that is, (x + y) (x — y) = x' — y'. 2. Twice the sum of two squares is equal to the sum of two... | |
 | William Smyth - 1855 - 370 σελίδες
...quantity, minus the double product of the first by the second, plus the second power of the second. 5. The product of the sum and difference of two quantities is equal to the difference of their second powers. The questions, art. 15, will furnish additional exercises for the learner in stating... | |
 | Harvey Goodwin - 1857 - 692 σελίδες
...following manner. It is easily seen by actual multiplication, that (a + 6) x (a - 6) = a- - b\ or that the product of the sum and difference of two quantities is equal to the difference of their squares; a theorem which may be used in the multiplication of such quantities as those in the last example,... | |
 | Joseph Ray - 1857 - 408 σελίδες
...3)2=25— 30+9=4. 2. 3. (3x— 5z)2=9 4. (02— 3ca:)2=a2z2— Gacxz+QcW. ART. 8O. THEOREM III. — The product of the sum and difference of two quantities, is equal to the difference of their squares. Let a represent one of the quantities, and i the other ; then o-|-i=their sum, and a — i=their difference.... | |
 | Elias Loomis - 1858 - 394 σελίδες
...beginners often commit the mistake of putting the square of a— b equal to a^—V. THEOREM III. (62.) The product of the sum and difference of two quantities...difference of their squares. Thus, if we multiply a+b By ab a'+ab -ab-b' We obtain the product a'—b'. EXAMPLES. 1. (2a+b) (2a-b)=. 2. (3a+4b) (3a-4b)=.... | |
 | William Smyth - 1858 - 344 σελίδες
...quantity, minus the double product of the first by the second, plus the second power of the second. 5. The product of the sum and difference of two quantities is equal to the difference of their second powers. The questions, art. 15, will furnish additional exercises for the learner in stating... | |
 | John Fair Stoddard, William Downs Henkle - 1859 - 538 σελίδες
...11, Square 2z-<"-1)yJ^J'-5«*L-1y I • w+nt-3 ..."M-"12, Square^ = y r— 4« THEOREM III. (111.) The product of the sum and difference of two quantities is equal to the difference of their squares. DEMONSTRATION. Let a + b and a—b represent respectively the sum and difference of two quantities.... | |
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