| Joseph Ray - Algebra - 1866 - 420 pages
...theorem. APPLICATION. 1. (2+5)2=4+20+25=49. 3. (ax+by)*=ax* -\-2abxy -\-by*. 4. ' 79. Theorem II. — The **square of the difference of two quantities is equal...of the first, minus twice the product of the first** ly the second, plus the square of the second. Let a represent one of the quantities, and 6 a — 6... | |
| Charles Davies - Algebra - 1866 - 316 pages
...(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...first by the second, plus the square of the second.** 1. Find the square of 2a — b. We have, (2a — b)2 = 4a2 — 4ab + b2. 2. Find the square of 4ac... | |
| Benjamin Greenleaf - 1866 - 338 pages
...+ 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 - Algebra - 1866 - 252 pages
...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'.... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...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—... | |
| Benjamin Greenleaf - 1867 - 336 pages
...a; y -\- y3. 3. Square 6 a2 -f- 2 a2 b. Ans. 4. Square o3 62 + 3 a> 6s c4. Ans. THEOREM II. 77i y^« **square of the difference of two quantities is equal...represent one of the quantities, and b the other; then,** (o — 6)' = (a — J) X (a — 6) = «' — 2 a 6 + 6', which proves the theorem. EXAMPLES. 1. Find... | |
| Charles Davies - Algebra - 1867 - 320 pages
...(a — 6)2 = (a — 6) (a — 6) = a2 — 2a6 + 62 : Thaf. is, The square of the difference between **two quantities is equal to the square of the first, minus twice the product of the first by** 1h* second, plus the square of the second. 1. Form the square of 2a — b. We have (2o- 6)2 = 4a2 -... | |
| Elias Loomis - Algebra - 1868 - 386 pages
...(5a+3Z>) 2 = 8. 4. (5a 2 +2&) 2 ^ 9. 5. (5a*+b) 2 = 10. 67. The square of the difference of two numbers **is equal to the square of the first, minus twice the...first by the second, plus the square of the second.** Thus, if we multiply a— b by a—b a 2 — ab - ab+b* we obtain the product a 2 —2ab+b 2 . EXAMPLES.... | |
| Horatio Nelson Robinson - 1868 - 430 pages
...second, plus the square of the second. II. (a— l)'=(a— ¿) (a— i) = a'— ïab+V Or, in words, The **square of the difference of two quantities is equal...of the first, minus twice the product of the first** and second, phis the square of the second. III. (a+l) (a_b)=a«_ £,' Or, in words, The product of... | |
| William Frothingham Bradbury - Algebra - 1868 - 264 pages
...y2. 2. 2x + 2y. Ans. 4 a;2 3. x+ 1. 4. 4 + a;. 5. 2x + 3y. Ans. 4z2-f6. 3a + 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 a and 6 represent the two quantities, and a ]> 6 ; their difference... | |
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