 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.  A Treatise on Algebra - Pągina 32per Elias Loomis - 1846 - 346 pąginesVisualització completa - Sobre aquest llibre
 | Horatio Nelson Robinson - 1863 - 432 pągines
...second, plus the square of the second. II. (a— b)'=(a— æ) (a— b)=a'— 2ab+b* Or, in words, The square of the difference of two quantities is equal to the square of the ßrst, minus twice the product of the first and second, plus the square of the second. III. (ti+6)... | |
 | Elias Loomis - 1864 - 386 pągines
...(5a'+&)'=. 10. (3+i)'=. most common mistakes of beginners is to call the square of a+b equal to a'+b'. THEOREM II. (61.) The square of the difference of...of the second. Thus, if we multiply a — b By a- b <£— ab - ab+b' We obtain the product a'—2ab+b'. EXAMPLES. 1. (a-2b)'=. 6. (7a'-&)'=. 2. (2a-3by=.... | |
 | Benjamin Greenleaf - 1864 - 336 pągines
...4 a4 62. 4. Square a5 62 + 3 a2 W c4. Ans. a6 64 4- 6 a" 6" c4 4- 9 a4 66 c8. ' THEOREM II. 77. ^%e square of the difference of two quantities is equal...of the first, minus twice the product of the first ty the second, plus the square of the second. For, let a represent one of the quantities, and b the... | |
 | Horatio Nelson Robinson - 1864 - 444 pągines
...(a— b) = at— 2ab+b' Or, in words, The square of the difference of two quantities is equal to tJie square of the first, minus twice the product of the first and second, plus the square of the second. III. O+&) (a— i)=a'— V Or, in words, The product of the sum and difference of two quantities is... | |
 | Paul Allen Towne - 1865 - 314 pągines
...numerical value when a; = 8, y = 8. 63. Since (*— y) ( x -y) = (x — yf = x'-2xy+y3, it follows that The square of the difference of two quantities is equal to the square of the first — twice their product -\- the square of the last. EXAMPLES. 1. (« — 6)" = ^ — 2a6 + 62. 2. (2a... | |
 | Joseph Ray - 1852 - 422 pągines
...proves the theorem AP PL I CAT ION. 1. (2+5)'=4+20+25=49. 2. (2m+ 3. ( 4. ( ART. 79. THEOREM II. — The square of the difference of two quantities is...of the first, minus twice the product of the first by the second, plus the square of the se'vnd. Let a represent one of the quantities, and b the other... | |
 | Benjamin Greenleaf - 1866 - 336 pągines
...+ 4 a4 ō2. 4. Square a3 b2 + 3 a2 a3 c4. Ans. a6 54 + 6 a5 55 c4 + 9 a4 #> c3. THEOREM II. 77t 7%e square of the difference of two quantities is equal...square of the first, minus twice the product of the firsl by the second, plus the square of the second. For, let a represent one of the quantities, and... | |
 | Joseph Ray - 1866 - 250 pągines
...a?—ab a2— 2a6-|-62 But a — b is the difference of the quantities, a and 6. Hence, ! Theorem II. — The square of the difference of two quantities is equal to the square of the first, minus twice the prodvet of the first by the second, phis the square of the second. 1. (5— 4)2=25— 40+16=1. 2. (2a—... | |
 | Joseph Ray - 1866 - 252 pągines
...a&+62 a?— 2a6+62 But a — b is the difference of the quantities, a and' 6. Hence, Theorem II. — The square of the difference of two quantities is equal to the square of the first, minus twice the prodnet of the first by the second, plus the square of the second. 1. (5— 4)2=25— 40+16=1. 2'.... | |
 | Charles Davies - 1866 - 314 pągines
...(a - b) (a- b) = a2- 2ab + P. That is, The square of the difference of any two quantities is eq^^al to the square of the first, minus twice the product of the first by the second, plus the square of the second. 1. Find the square of 2a — b. We have, (2a — b)2... | |
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