| Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...difference. By actual multiplication we learn that (A + B) 2 =(A + B)(A + B)'=A l + 2AB + B\ which means that the square of the sum of two quantities is equal to...square of the first, plus twice the product of the first and second, plus the square of the second. Likewise we learn that which means that the square... | |
| 1882 - 328 pages
...theorem? 4. What is a factor? 5. What is a co-efficient? 6. Prove that the square of the sum of any 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. 7. Show that — 2a subtracted from 3a leaves 5a.... | |
| James Bates Thomson - Algebra - 1884 - 334 pages
...31. Expand (x + y + z] (:;• + y + 0). THEOREMS AND FORMULAS. 101. THEOREM i. — The Square of flic Sum of two quantities is equal to the square of the first, plus twice their product, plus the square of the second. i. Let it be required to multiply a+ b into itself. ANALYSIS.... | |
| Webster Wells - Algebra - 1885 - 370 pages
...ab a?+2ab + b2 a2-2a6 + 62 a2 -b2 In the first case, we have (a-)- 6)2 = a2 + 2ab + b2. (1) That is, the square of the sum of two quantities is equal to...product of the two, plus the square of the second. In the second case, we have (a — 6)2 = a2 — 2 ab + 62. (2) That is, the square of the difference... | |
| Webster Wells - Algebra - 1885 - 324 pages
...a& a2+2ab + b2 a?—2ab + b2 a2 —b2 In the first case, we have (a+&)2 = а2 +2ab+b2. (1) That is, the square of the sum of two quantities is equal to...product of the two, plus the square of the second. In the second case, we have (a — &)2 = a2— • 2 ab + b2. (2) That is, the square of the difference... | |
| Webster Wells - 1885 - 368 pages
...cP+-2ab + b2 a2-2a6 + 62 a2 — 62 In the first case, we have (a+ 6)2 = a2 + 2a6 + b2. (1) That is, the square of the sum of two quantities is equal to...product of the two, plus the square of the second. In the second case, we have (a — 6)2 = a2-— 2 ab + b2. (2) That is, the square of the difference... | |
| Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1885 - 412 pages
...multiplication we have =o2 — 2a¿> + 62 (2). These results are embodied in the following rules : RULE 1. The square of the sum of two quantities is equal to the sum of their squares increased by twice their product. RULE 2. The square of the difference of two... | |
| Webster Wells - Algebra - 1885 - 372 pages
...That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference... | |
| Algebra - 1888 - 492 pages
...multiplication that are important on account of their frequent occurrence in algebraic operations. 85. I. The square of the sum of two quantities is equal to...square of the first, plus twice the product of the first by the second, plus the square of the second. Thus, (x + y)2 = ж2 + 2xy + y2. (x + 3)2 = ж2... | |
| Webster Wells - Algebra - 1889 - 584 pages
...—ab — b2 a?—2ab + b2 cr — b2 In the first cas.e, we have (a+&)2 = a2 + 2ab +&2. (1) That is, the square of the sum of two quantities is equal to...product of the two, plus the square of the second. In the second case, we have (a — b)2 = a? — 2 ab + &2. (2) That is, the square of the difference... | |
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