 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.  A Treatise on Algebra - Page 37by Elias Loomis - 1846 - 346 pagesFull view - About this book
 | 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 the 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... | |
 | James Bates Thomson - Algebra - 1880 - 324 pages
...the same Jetter f JOQ. How indicate the mn]tiplicatipn of polynoiniale ? THEOREMS AND FORMULAS. 101. THEOREM i. — The Square of the Sum of two quantities is equal to the square of the first, plus twice their product, plus the square of the second. i. Let it be required to multiply a+ b into itself. ANALYSIS.... | |
 | 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,... | |
 | Joseph Ray - Arithmetic - 1880 - 420 pages
...operations illustrate the following principle : PRINCIPLE. — 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. Thus : Show by involution, that : \. (5)2... | |
 | 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 to the 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.... | |
 | James Mackean - 1881 - 510 pages
...much simplified and shortened. I. Multiply а + b by itself. а + b а + b a2+ ob ab + b2 . That is, the square of the sum of two quantities is equal to the sum of the squares of the quantities increased by twice their product. II. Multiply а - b by itself.... | |
 | Edward Olney - Algebra - 1882 - 358 pages
...partial products as they stand, even without first adding the products by « and 6. QED 83. THEO. — The square of the sum of two quantities is equal to the 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... | |
 | Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...difference. By actual multiplication we learn that (A + B) 2 =(A + B)(A + B)'=A l + 2AB + B\ which means that 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. Likewise we learn that which means that the... | |
 | 1882 - 328 pages
...theorem? 4. What is a factor? 5. What is a co-efficient? 6. Prove that the square of the sum of any 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. 7. Show that — 2a subtracted from 3a leaves... | |
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