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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. "
Normal Arithmetic: A Text-book, Theoretical and Practical, in Six Parts ... - Σελίδα 230
των Silas Lawrence Loomis - 1859 - 300 σελίδες
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Elements of Algebra

William Smyth - 1830 - 278 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 <tb +...

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

Bourdon (M., Louis Pierre Marie) - 1831 - 446 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 third; plus...

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

Charles Davies - 1835 - 378 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...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...

Elements of Algebra

1838 - 372 σελίδες
...the binomial, (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...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...

First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - 1839 - 264 σελίδες
...the binomiaj (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...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 = 4<z3 + 12ab + 962. 2. (5a6 + 3<zc)2...

Elements of Algebra

1839 - 368 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 by a —...

Elements of Algebra

Bourdon (M., Louis Pierre Marie) - 1839 - 368 σελίδες
...binomial, (a-\-b). We have, from known principles, That is, the square ofthe sum of two quantities is equal to the square of the first, plus twice the product of tl>e first by the second, plus the square of the second. Thus, to form the square of 5a2+8a26, we have,...

Gradations in Algebra in which the First Principles of Analysis are ...

Richard W. Green - 1839 - 156 σελίδες
...their sum. a+b a+b a3+ab +ab+b3 By this operation we find the following general property. The square of the sum of two numbers is equal to the square of the Jlrst number, plus twice the product of the two numbers, plus the square of the last number. §173....

First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - 1840 - 264 σελίδες
...the binomial (a+6). 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 frst by the second, plus the square of the second. 1. Form the square of 2a+3J. We have from the rule...

Elements of Algebra

Charles Davies - 1842 - 368 σελίδες
...known 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...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 2 i) 2...




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