| Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...second, plus the square of the second. II. (a — b)*=(a—b)(a — b) = a*—2ab + & ; hence, 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. III. (a +b)(a — b)—a*-^; hence, Tue product of the sum... | |
| William Guy Peck - Algebra - 1875 - 348 pages
....product of the first and second, plus the square of the second. 2°. The square of the difference of any **two quantities, is equal to the square of the first, minus twice the product of the first** and second, plus the square of the second. 3°. The product of the sum and difference of any two quantities,... | |
| Lorenzo Fairbanks - 1875 - 468 pages
...is a quantity consisting of two terms, and its square is equal to the square of the first term, plus **twice the product of the first by the second, plus the square of the second.** Let 35 be written 30 + 5. Then, squaring this number, by multiplying each part separately, we hare,... | |
| Charles Mansford - 1875 - 110 pages
...square of the first + twice the product of two quantities + the square of the second. And from (ii.) The **square of the difference of two quantities is equal to the square of the first** — twice the product of the quantities + the square of the second. Twice Sq. of Sq. of first. the... | |
| Benjamin Greenleaf - 1876 - 334 pages
...36a4-f-24a4» + 4a4i2. 4. Square o? & + 3 a2 63 c4. Ans. a6 64 + 6 a5 i5 c4 -f- 9 a4 If c3. THEOREM II. 77, The **square of the difference of two quantities is equal...second, plus the square of the second. For, let a** repreient one of the quantities, and b the other; then, (a — 6)2 = (a — 6) X (a — 6) = a2 —... | |
| Charles Davies - Algebra - 1876 - 324 pages
...we have, (a - o)2 = (a - &) (a - o) = a2 - 2ao + ó2. That is, 7%e square of (he difference of any **two quantities is equal to the square of the first, minus twice the product of** theßrst by the second, plus the square of the second. 1. Find the square of 2a — b. We have, (2a... | |
| William Frothingham Bradbury - Algebra - 1877 - 280 pages
...4x2+ 8x 3. a; + 1. 4. 4 + *. 5. 2x + 3y. Ans. 4 *2 4-1? xy + 9 /. 6. Зa + 6. THEOREM III. 59. 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. Let о and b represent the two quantities, and a ]> b ; their dii... | |
| Edward Olney - Algebra - 1877 - 468 pages
...За*Ь'-. Result, 25а - " + ЗОаб» + б. Square $aö-« + $a:-'b-'. ßesult, 93, THEO. — Tlœ **square of the difference of two quantities is equal to the square of the** ßrst, minus twice the product oftheßrut by tlie second, plus Die square of the second. DEM. — Let... | |
| Benjamin Greenleaf - Algebra - 1877 - 662 pages
...quantities is equal to the square of the first, plus twice the product of the first by the second, plus tlte **square of the second. For, let a represent one of the quantities, and** i the other ; then, (« + i)' = (a -f- 1) x (a + b) = a2 + 2 ai + V. Hence, the theorem is true. •... | |
| Edward Olney - 1878 - 362 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... | |
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