| William Smyth - Algebra - 1830 - 264 pages
...power or square of the sum of two quantities contains the square of the first quantity, plus double **the product of the first by the second, plus the square of the second.** Thus, (7 + 3) (7 + 3) or, (7 + 3)' = 49 + 42 + 9 = 100 So also (5 a2 + 8 a2 6)2 = 25 a6 + 80 <tb +... | |
| Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 389 pages
...enunciated in another manner : viz. The square of any polynomial contains the square of the first term, **plus twice the product of the first by the second, plus the square of the second;** plus twice the product of each of the two first terms by the third, plus the square of the third; plus... | |
| Charles Davies - Algebra - 1835 - 374 pages
...principles, (a+by=(a+b) (a+b)=a3+'2ab+b3. That is, the square of the sum of two quantities is composed of **the square of the first, plus twice the product of...first by the second, plus the square of the second.** Thus, to form the square of 5a3+8a3i, we have, from what has just been said, 2d. To form the square... | |
| Algebra - 1838 - 372 pages
...use in algebra. 1st. Let it be required to form the square or second power of the binomial, (a+*)- **We have, from known principles, That is, the square...first by the second, plus the square of the second.** Thus, to form the square of 5a"-\-8a2b, we have, from what has just been said, 2d. To form the square... | |
| Charles Davies - Algebra - 1839 - 272 pages
...second power of the binomial (a+6). We have, from known principles, (a+b)2=(a+b) (a+b)=a? + 2ab+b\ **That is, the square of the sum of two quantities is...of 2a+36. We have from the rule (2a + 36)2 — 4a2** + 12ab + 962. 2. (5a6+3ac)2 = 25a2Z-2+ 30a26c+ 9aV. 3. (5a2+8a26)2~=25a4 + 80a46 +64a462. 4. (6ax +... | |
| Algebra - 1839 - 368 pages
...second power of the binomial, (a-\-b). We have, from known principles, (a+by=(a+b) (a+i)=a3+2ai+i3. **That is, the square of the sum of two quantities is...first by the second, plus the square of the second.** Thus, to form the square of 5a3+8a3i, we have, from what has just been said, (5a3+8a3i)3==25o4+80a4i+64o4i3.... | |
| Charles Davies - Algebra - 1839 - 252 pages
...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 the second, plus the square of the second. 1 Form the square of** 2a — b. We have (2<z — 6)2=±4a2— 4a6 + 62. 2. Form the square of 4ac — be. We have 3. Form... | |
| Charles Davies - Algebra - 1840 - 252 pages
...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 the second, plus the square of the second.** ] Form the square of 2a— b. We have (2o — 6)2 = 4a2 - 4a b + b2. 2. Form the square of 4ac —... | |
| Charles Davies - Algebra - 1840 - 264 pages
...of the sum of two quantities is equal to the square of the first, plus twice the product of the frst **by the second, plus the square of the second. 1. Form the square of** 2a+3J. We have from the rule (2d + 3*)2 = 4a2 + IZab + 9b*. 2. (5a6 + 3ac)2 = 25a2i2+ 30a2Je+ 9aV.... | |
| Charles Davies - Algebra - 1841 - 264 pages
...second power of the binomial (a+J). We have, from known principles, (a+J)2=(a+J) (a+J)=a2-f 2aJ+62. **That is, the square of the sum of two quantities is...plus the square of the second. 1. Form the square of** 2a+3J. We have from the rule (2o + 3J)2 = 4a2 + 12ab + 9J2. 2. (5aJ+3ac)2 = 25a2J2+ 30a2Jc+ 9a2c2.... | |
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