 | Gerardus Beekman Docharty - 1862 - 336 σελίδες
...Multiply a— b by a— b. (a-by=(ab) (ab) = a'-2ab+b\ From which we deduce the following 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 (he second. EXAMPLES. 2. (3x-2a)'=(3x-2a)(3x-2a). Ans. 3. (9x-3y)'=... | |
 | Horatio Nelson Robinson - 1863 - 432 σελίδες
...second, plus the square of the second. II. (a— b)'=(a— ¿) (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)... | |
 | Benjamin Greenleaf - 1864 - 336 σελίδες
...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 σελίδες
...(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... | |
 | Elias Loomis - 1864 - 386 σελίδες
...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. Thus, if we multiply a + b By a + b a'+ ab _ _ We obtain the product a'+2ab+b'. Hence, if we wish to obtain the square of a binomial, we can write... | |
 | Paul Allen Towne - 1865 - 314 σελίδες
...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 σελίδες
...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 σελίδες
...+ 4 a4 ô2. 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 σελίδες
...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 σελίδες
...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'.... | |
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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. 
