 | Charles Davies - Algebra - 1876 - 324 pages
...+ b, we have, (a + by = (a + b) (a + b) = a1 4- ЧаЪ 4- *'. That is, The square of the sum of any two quantities is equal to the square of the first, plus twice the product of theßrst by the second, plus the square of the second. 1. Find the square of la + Sb. We have from... | |
 | Benjamin Greenleaf - Algebra - 1877 - 662 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...twice the product of the first by the second, plus tlte square of the second. For, let a represent one of the quantities, and i the other ; then, («... | |
 | Edward Olney - Algebra - 1877 - 466 pages
...(m + n)(m + n) — (m — n) (m — n). Last Besvlt, 4mn. THREE IMPORTANT THEOREMS. 94. THEOREM. — 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. DEM. — Let x be any one quantity and y any other. The sum is... | |
 | William Frothingham Bradbury - Algebra - 1877 - 280 pages
...difference 5x2 — 3y. 6. Sum 2 a — 8 b and difference 10 a + 14 6. THEOREM II. .'»S. The square of /he 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. Let a and b represent the two quantities ; their sum will be a-fu.... | |
 | Edward Olney - Algebra - 1878 - 516 pages
...n)(m + n) — (TO — n) (m — n). Z/osi Result, 4.mn, THREE IMPORTANT THEOREMS. 04:. THEOREM. — 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. DEM. — Let x be any one quantity and y any other. The sum is... | |
 | Edward Olney - 1878 - 360 pages
...products as they stand, even without first adding the products by a and 6. 4. ED 85. THEO. — Tlie 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 is... | |
 | James Bates Thomson - Algebra - 1878 - 322 pages
...+ 5"). 31. Expand (x + y + z) (x + y + z). GENERAL PRINCIPLES AND FORMULAS OF MULTIPLICATION. 101. 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.... | |
 | John Stewart (of Hastings.) - Algebra - 1878 - 128 pages
...¡x2y + 3*У + у. ix. (x — у)» = x3 — yс1y + усy2 — y3. i. (a + b) (a + ¿) = a" + P + 2ab. The Square of the sum of two quantities is equal to the sum of the squares of each of the quantities increased by twice the product. Write down the squrtres... | |
 | 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... | |
| |
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. 
