| 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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