 | Elias Loomis - Algebra - 1868 - 312 pages
...most common mistakes of beginners is to call the square of a+b equal to a'+b'. THEOREM II. (66.) The square of the difference of two quantities is equal to the square of the first, minus twice theprod~ net of the first and second, plus the square of the second. Thus, if we multiply a —b by... | |
 | Robert Wallace - 1870 - 164 pages
...Iheorem for finding the square of the difference of any two quantities is deduced. THEOREM II. — The square of the difference of two quantities is equal...first by the second, plus the square of the second. EXAMPLES. 1. 2. 3. 4. 5. **. 'J — ~4f — "g Y~TTn — r44 x — y)2=(x — y] (xy)=x2 — 2xy-\-y-.... | |
 | Joseph Ray - Algebra - 1866 - 420 pages
...the theorem. APPLICATION. 1. (2+5)2=4+20+25=49. 2. (2m+3n)2=4m2-f I2wm+9n2. 79. Theorem II. — The square of the difference of two quantities is equal...first by the second, plus the square of the second. Let a represent one of the quantities, and 6 a — 6 the other. a — b Then, a — 6= their difference;... | |
 | Benjamin Greenleaf - Algebra - 1871 - 412 pages
...square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (2) That is, The square of the difference of two quantities is equal...first by the second, plus the square of the second. Also, (a _|- 5) (a — 5) = a2 — 52. (3) That is, jTAe product of the sum and difference of two quantities... | |
 | Joseph W. Wilson - Algebra - 1873 - 268 pages
...a fl2 , ^~ + b by itself, we have what the theorem ' ab + V states. as + 2 ab + b2 Theorem II. The square of the difference of two quantities is equal...of the first, minus twice the product of the first and second, plus the square of the second. a — b PROOF. Let a and b stand for any a — b two quantities.... | |
 | Edward Olney - Algebra - 1873 - 354 pages
...square of the first, plus twice the product of the two, plus the square of the second. 86. THEO. — The square of the difference of two quantities is equal...square of the first, minus twice the product of the two, plus the square of the second. 87. THEO. — The product of the sum and difference of two quantities... | |
 | David White Goodrich - Ready-reckoners - 1873 - 220 pages
...3969, etc. Again, since (a— by=a' — 2«5-t-6", the square of the difference of two numbers equals the square of the first, minus twice the product of...first by the second, plus the square of the second. Thus 19" = 400—40+2 = 361. 95" = 10000—1000+25 = 9025. 85'= 8100— 900+25 = 7225. 57"= 3600- 360+... | |
 | Elias Loomis - Algebra - 1873 - 396 pages
...(5a3+8a26)2= 3. (5a+36)2= 8. 4. (5a2+ 26)2= 9. 5. 5a3+i= 10. 67. T/ie square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the sec~ and, plus the square of the second. Thus, if we multiply a— 6 by a— b a?— ab - ab+bz we... | |
 | Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...Ex. 1. Show that the square of the 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. 2. Eesolve 9a2 — 6ac + c2 into two equal factors. 3. Show that the difference of any two equal powers... | |
 | Benjamin Greenleaf - Algebra - 1875 - 338 pages
...a4 + 24 aU 4- 4 a4 #". 4. Square a3 62 + 3 a2 V c\ Ans. a"64+6a5J5c4 + 9a4isc». THEOREM II. IT, The square of the difference of two quantities is equal...the first, minus twice the product of the first by th» second, plus the square of the second. For, let a represent one of the quantities, and 6 the other... | |
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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. 
