Books Books That is, 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. Elementary Algebra: Embracing the First Principles of the Science - Page 25
by Charles Davies - 1842 - 258 pages ## New Elementary Algebra: in which the First Principles of Analysis are ...

Benjamin Greenleaf - 1863 - 338 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...first by the second, plus the square of the second. For, let a represent one of the quantities, and b the other; then, (a + ft)2 = (a -f- 6) X (a + 6)... ## Elements of arithmetic, tr. by J. Spear

Charles Auguste A. Briot - 1863 - 376 pages
...SUM OF TWO NUMBERS. 156. The square of the sum of two numbers equals the square of the first number, plus twice the product of the first by the second, plus the square of the second. Be it given to raise the sum of 7 + 5 to the square ; it is necessary to multiply 7 + 5 by 7 + 5. In... ## The Institutes of Algebra: Being the First Part of a Course of Mathematics

Gerardus Beekman Docharty - Algebra - 1862 - 338 pages
...THEOREM II. The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of (he second. EXAMPLES. 2. (3x-2a)'=(3x-2a)(3x-2a). Ans. 3. (9x-3y)'= Ans. 4. (6-i)'= Ans. 5. (Gt)'=... ## Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - Algebra - 1866 - 252 pages
...a2+2a6-j-62. Thus: a+6 a+6 a2+2a6-|-62 But a+6 is the sum of the quantities, a and 6. Hence, Theorem I. — The square of the sum of two quantities is equal to...first by the second, plus the square of the second. NOTE . — Let the pupil apply the theorem by writing the following examp\>, enunciated thus : What... ## New Elementary Algebra

Benjamin Greenleaf - 1866 - 336 pages
...algebraic operations. THEOREM I. 76, The square of the sum of two quantities is equal to the tquare of the first, plus twice the product of the first by the second, plus the square of the second. For, let a represent one of the quantities, and b the other; then, (a + 6)' = (a + 6) X (a + V) = a3... ## Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1852 - 420 pages
...THEOREM II. — The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the se'vnd. Let a represent one of the quantities, and b the other ; then a — 6=their difference ; and... ## Ray's Algebra, First Book: Primary Elements of Algebra, for Common Schools ...

Joseph Ray - Algebra - 1866 - 252 pages
...square of the difference of two quantities is equal to the square of the first, minus twice the prodnet of the first by the second, plus the square of the second. 1. (5— 4)2=25— 40+16=1. 2'. (2a— 6)2=4a2— 3. (3a!— 2yy=9x*-— 4. (x*— y*y=tf 5. (ax— *-)2=aV—... ## Elementary Algebra

Charles Davies - Algebra - 1867 - 320 pages
...6) = a2 + 2a5 f- b\ That is, The square &f the sum of two quantities is equal to the tqitart •)f the first, plus twice the product of the first by the second, plat the square of the second. 1. Form the square of 2a + 36. We have from the rule (2a + 36)2 = 4a2... ## A Treatise on Algebra

Elias Loomis - Algebra - 1868 - 386 pages
...2 = 10. 67. The square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second. Thus, if we multiply a— b by a—b a 2 — ab - ab+b* we obtain the product a 2 —2ab+b 2 . EXAMPLES.... 