 | Benjamin Greenleaf - Algebra - 1879 - 376 pages
...following theorems give rise to formulas, useful in abridging algebraic operations. THEOREM I. 76, The square of the sum of two quantities is equal to...the first, plus twice the product of the first by th« second, plus the square of the second. Define a Formula. What is Theorem I. ? For, let a represent... | |
 | Elias Loomis - Algebra - 1879 - 398 pages
...The three following theorems have very important applications. 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 Hie square of the second. Thus, if we multiply a+b by a + b a? + ab ab + b2 we obtain the product a2... | |
 | Shelton Palmer Sanford - Algebra - 1879 - 348 pages
...to do so. A PROBLEM is a question proposed for solution; i. a something to be done. TIIEOEEM I. 67. The square of the SUM of two quantities is equal to the square of the first, plus twice lhe product of the first by the second, plus the square of the second. Ex. 1. What is the square of... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...= (a + V) (a + I) ; whence, by actual multiplication, we have That is, (a + bY = a? + 2ab + b2. (1) The square of the sum of two quantities is equal to the square nf the first, plus twice the product of the first by the second, plus the square of the second. 105.... | |
 | Benjamin Greenleaf - Algebra - 1879 - 350 pages
...following theorems give rise to formulas, useful in abridging algebraic operations. THEOREM I. 76, The square of the sum of two quantities is equal to the tguare of the first, plus twice the product of the first by the second, plus the square of the second.... | |
 | Edward Olney - Algebra - 1880 - 354 pages
...products as they stand, even without first adding the products by a and u. Ч К. D. 85. THEO. — The square of the sum of two quantities is equal to...square of the first, plus twice the product of the two, plus the square of the second. 86. THEO. — The square of the difference of two quantities is... | |
 | Webster Wells - Algebra - 1880 - 498 pages
...= (a + b) (a + b) ; whence, by actual multiplication, we have That is, (a + b)2 = a2+2ab + b2. (1) The square of the sum of two quantities is equal to the square of the first, plus t1cice the product of the first by the second, plus the square of the second. 105. We may also show,... | |
 | Charles Scott Venable - Algebra - 1880 - 168 pages
...expresses in algebraic language the following Rule. — The square of the sum of two quantities is the square of the first, plus twice the product of the first by (he second, plus the square of the second. Ex. 1. (ж + 5)' = x' + Wx + 25. Ex. 2. (За + 20)' = (За)'... | |
 | Joseph Ray - Arithmetic - 1880 - 420 pages
...following principle : PRINCIPLE. — The square of the sum of two numbers is equal to the square of Hie first, plus twice the product of the first by the second, plus tiie square of the second. Thus : Show by involution, that: 1. (5)2 equals 25. 8. a)5 equals ttm2.... | |
 | Edward Olney - Algebra - 1881 - 506 pages
...also (m+n)(m+n) — (m— n)(m— n). Last result, 4ww. THEEE IMPORTANT THEOREMS. .94. Theorem. — The, square of the sum of two quantities is equal...square of the first, plus twice the product of the two, plus the square of the second. Demonstration. — Let x be any one quantity and y any other. The... | |
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The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second. 
