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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. "
Arithmetic and Its Applications: Designed as a Text Book for Common Schools ... - Σελίδα 330
των Dana Pond Colburn - 1856 - 366 σελίδες
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Elements of Algebra

William Smyth - 1830 - 264 σελίδες
...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...

Elements of Algebra: Tr. from the French of M. Bourdon, for the Use ..., Τόμος 1

Bourdon (M., Louis Pierre Marie) - 1831 - 389 σελίδες
...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...

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

Charles Davies - 1835 - 353 σελίδες
...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 the 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...

Elements of Algebra

1838 - 358 σελίδες
...(a+*)- We have, from known principles, 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. Thus, to form the square of 5a"-\-8a2b, we have, from what has just been said, 2d. To form...

First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - 1839 - 252 σελίδες
...principles, (a+b)2=(a+b) (a+b)=a? + 2ab+b\ 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. 1. Form the square of 2a+36. We have from the rule (2a + 36)2 — 4a2 + 12ab + 962. 2. (5a6+3ac)2...

Elements of Algebra

1839 - 355 σελίδες
...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. Thus, (7o3i3— 12ai3)3=49o4i4— 168a3i5+144a3i6. 3d. Let it be required to multiply a-\-b...

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

Charles Davies - 1839 - 252 σελίδες
...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...

Elements of algebra

William Foster - 1840 - 80 σελίδες
...ab —аЬ—Р a'+2aó+6* o'— 2a6+6* a* * —6' Hence 1 . The square of the sum of two quantities equals the square of the first, plus twice the product of the quantities, plus the square of the second. 2. The square of the difference of two quantities equals...

Elements of Algebra

Charles Davies - 1842 - 358 σελίδες
...principles, (a + b)2=(a+b) (a+i)=a 2 +2ai+i 2 . 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. Thus, to form the square of 5o 2 +8a 2 i, we have, from what has just been said, (5a 2 + 8a...

Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - 1842 - 258 σελίδες
...(a-\-b). We have, from known principles, 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. 1. Form the square of 2a+36. We have from the rule (2a + 36)2 = 4a2 + 12a6 + 962. 3. (5a6+3ac)2...




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