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" That is, the square of the sum of 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. "
Elementary Algebra: Embracing the First Principles of the Science - Page 25
by Charles Davies - 1842 - 258 pages
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Elements of Algebra

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 +...
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Elements of Algebra: Tr. from the French of M. Bourdon, for the ..., Volume 1

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...
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Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

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...
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Elements of Algebra

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...
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First Lessons in Algebra: Embracing the Elements of the Science

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 +...
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Elements of Algebra

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....
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First Lessons in Algebra, Embracing the Elements of the Science ...

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...
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First Lessons in Algebra: Embracing the Elements of the Science

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 —...
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First Lessons in Algebra: Embracing the Elements of the Science

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....
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First Lessons in Algebra: Embracing the Elements of the Science

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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