 | G. Ainsworth - 1854 - 216 pages
...difference of two numbers is equal to the difference of their squares. II. (a + b}*=a? + 2ab + b2 ; that is, The square of the sum of two numbers is equal to the sum of their squares, plus twice their product. III. (a— b)2=ai— Zab + b2 ; that is, The square... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...two examples are comprehended under the rule in Art. 60, that 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. Ex. 3. Required the cube of ^/x+3^/y. Ex. 4. Required the fourth... | |
 | George Roberts Perkins - Arithmetic - 1855 - 388 pages
...=:902+2x90.3+32=8100+540+ 9. 482=(40+8)2=403+2x40.8 + 82= 1600+640+64. From the above, we draw the following property : The square of the sum of two numbers is equal to the square of the first number, plus twice the product of the first number into the second, plus the square of the teeond.... | |
 | Dana Pond Colburn - Arithmetic - 1855 - 396 pages
...the second, and b2 equals the square of the second ; The square of the sum of any two numbers equals the square of the first, plus twice the product of the first by the second, plus the square of the tecond. Illustrations. (7 + 5)2 = 72 + 2 X 7 X 5 + 52 = 49 + 70 + 25... | |
 | John Radford Young - 1855 - 218 pages
...a +6 a —6 a'— aft a +6 a -6 (a + b)(ab) -ab-V ' -ft' From these three results, we learn that 1. The square of the sum of two numbers is equal to the squares of the numbers themselves plus twice their product. 2. The square of the difference of two... | |
 | Dana Pond Colburn - Arithmetic - 1856 - 392 pages
...the second, and b2 equals the square of the second ; The square of the sum of any two numbers equals the square of the first, plus twice the product of the first by the second, plus the square of the tecond. Illustrations. (7 + 5)2 = 72 + 2 X 7 X 5 + S2 = 49 + 70 + 25... | |
 | Elias Loomis - Algebra - 1856 - 280 pages
...that they should be carefully committed to memory. THEOREM I. The square of the sum of two quantities is equal to the square of the first, plus twice the product oj the first by the second, plus the square of the second. Thus, if we multiply a +b by a +b a'+ ab... | |
 | Joseph Ray - Algebra - 1857 - 408 pages
...the simplest application of Algebra. ART. 78. THEOREM I. — 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. Let a represent one of the quantities, and b the other ; then... | |
 | Richard Dawes - Teaching - 1857 - 272 pages
...their difference is equal to the difference of their squares. (2.) That (a + 6)2 = aa+2aJ+62, or that the square of the sum of two numbers is equal to the sum of their squares, increased by twice their product. (3.) That (a— 6)2=a2 — 2o6 + 4= = a" +... | |
 | Daniel Leach - 1857 - 314 pages
...402=1600 2(40x5)=400 52=25 1600+400+25=2025 284. From the preceding illustration it is evident that the square of the sum of two numbers is equal to the squafe of the two numbers, plus twice their product, or. to the square of the tens, plus the square... | |
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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. 
