 | 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 - 314 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 - 336 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 - 250 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 - 322 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... | |
| |
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. 
