 | James Thomson - 1880 - 408 pages
...accuracy necessary in the result may require. The principle on which the preceding rule depends, is, that the square of the sum of two numbers is equal to the sum of the squares of the numbers added to twice their product. Thus, 34 being = 30 + 4, its square... | |
 | George Albert Wentworth - Algebra - 1881 - 406 pages
...three which follow are of great importance: From (1) we have (a + bf = a? + 2ab + b2. That is, 74. The square of the sum of two numbers is equal to the sum of their squares + twice their product. From (2) we have (a — 6)2 = a' — 2 ab + 62. That is,... | |
 | Homersham Cox (the younger) - 1885 - 248 pages
...added units. We shall soon require the following important theorem relating to the squares of numbers. The square of the sum of two numbers is equal to the sum of the squares of the number together with twice the product of the numbers. For instance 1 1 is... | |
 | George Albert Wentworth - Algebra - 1886 - 284 pages
...follow are of great importance : Ь' à2 - Ь2 From (1) we have (a + ¿)2 = a2 + 2ab + V. That is, 74. The square of the sum of two numbers is equal to the sum of their squares + twice their product. From (2) we have (a - ¿)2 = a2 — 2 ab + b\ That is,... | |
 | Edward Albert Bowser - Algebra - 1888 - 868 pages
...a + 6 we get (« + 6) (a + 6) = «2 + 2a6 + 62 ; that is (a + 6)2 = a2 + 2«6 + 62. . . . (1) Thus the square of the sum of two numbers is equal to the sum of the squares of the two numbers increased by twice their product. Similarly, if we multiply a... | |
 | William Frothingham Bradbury, Grenville C. Emery - Algebra - 1889 - 428 pages
...already established we are prepared to demonstrate the following important theorems. THEOREM I. 85. The square of the sum of two numbers is equal to the square of the first, plus twice the product of tlie two, plus the square of tlie second. PROOF. Let a and b represent any... | |
 | Webster Wells - Algebra - 1890 - 604 pages
...(Art. 8), (a + by = a2 + 2ab + b2. (1) This formula is the symbolical statement of the following rule : The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second. In the second case,... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...triangle having AB = AC, and if D be taken in AC so that BD = BC, prove that the square on BC = AC X CD. * The square of the sum of two numbers is equal to the sum of the squares <jf the two numbers increased by twice their product. Proposition 28. Theorem. 333.... | |
 | John Henry Walsh - 1893 - 426 pages
...Multiplying by 20 202 + 20 X 5 Multiplying by 5 20 x 5 +5' 202 + 2(20 x 5) + 5' = 400 + 200 + 25 = 625. 1032. The square of the sum of two numbers is equal to the square of the first + twice the product of the first by the second + the square of the second. 132=(10 + 3)2 = 102+2(10x3)+32=?... | |
 | Eugene L. Dubbs - Arithmetic - 1893 - 244 pages
...is an easy and elegant method of squaring numbers less than 100, by using an algebraic theorem : " The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first by the seccond, plus the square of the second." Square 45 by the... | |
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That is, the square of the sum of two numbers is equal to the square of the first number, plus twice the product of the two numbers, plus the square of the second number. 
