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" 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 second. "
New Elementary Algebra: Designed for the Use of High Schools and Academies - Page 54
by Benjamin Greenleaf - 1879 - 309 pages
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New Practical Algebra: Adapted to the Improved Methods of Instruction in ...

James Bates Thomson - Algebra - 1878 - 324 pages
...a-' + 2ab + V. a + rtO Hence, the + ab + b3 FORMULA, (a+b)9 = <P+2db-\-&. Ans. a' + tab + b9 102. The square of the difference of two quantities is equal to the square of the first, minus twice their product, plus the square of the second. 2. Let it be required to multiply a — b by a — b....
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The Complete Algebra: Embracing Simple and Quadratic Equations, Proportion ...

Edward Olney - Algebra - 1878 - 516 pages
...+ 3a3s. jfesutt, 25a - 4 + 30o6 + 9a<*. 5. Square ^16 - * + fa? -' 6 - '. 95. THEO. — Tlve square of the difference of two quantities is equal to the square of tlie first, minus twice the product of the first by tlie second, plus the square of the second. DEM....
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New Elementary Algebra: Designed for Common and High Schools and Academies

Shelton Palmer Sanford - Algebra - 1879 - 348 pages
...point, and, multiply ing a2+2a6 + 62 by (a -H6), he will have the expansion required* THEOKEM H. 68. The square of the DIFFERENCE of two quantities is equal...first by the second, plus the square of the second. Ex. 1. Find the square of (a — 6). Analysis. Here a and 6 are the two quantities, and OPERATION (a...
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University Algebra

Webster Wells - Algebra - 1879 - 468 pages
...second. 105. "We may also show, by multiplication, that (a — 6)2 = a2 — 2 ab + b2. (2) That is, The square of the difference of two quantities is equal to the square of the first, minus twice thg product of the first by the second, plus the square of the second. 106. Again, by multiplication,...
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New Elementary Algebra

Benjamin Greenleaf - 1879 - 348 pages
...sum and difference of two >'quanti- . f • ties is equal to the difference of their squares. .stet'f For, let a represent one of the quantities, and b the other ; -• '^^u, then, (a + 6) X(<>-6)-4> — P. which agrees with the theorem. EXAMPLES. 1. Find the product...
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Elementary Algebra: Designed as a First Book of Algebra for All Grades of ...

Thomas K. Brown - Algebra - 1879 - 292 pages
...in which we cannot tell at once what the root is. Theorems I. and II. are, The square of the gum or difference of two quantities is equal to the square of the first, =t twice the product of the first and second, + the square of the second. Therefore we first take the...
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University Algebra: Designed for the Use of Schools and Colleges

Webster Wells - Algebra - 1880 - 512 pages
...the second. 105. We may also show, by multiplication, that (a - b)2 = a2-2ab + b2. (2) That is, The square of the difference of two quantities is equal...first by the second, plus the square of the second. 106. Again, by multiplication, we have (a + b) (a - b) = a2 - V. (3) That is, The product of the sum...
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An Easy Algebra for Beginners: Being a Simple, Plain Presentation of the ...

Charles Scott Venable - Algebra - 1880 - 168 pages
...Zab + V. . . . (B), which expresses the Rule :—Tlie square of the difference of two quantities is the square of the first, minus twice the product of...first by the second, plus the square of the second. Ex. 1. (x - 5)" = x' - 10ж + 25. Ex. 2. (За - 2o)" = (За)' - 2 x За х 2o + (2o)' = 9a' - 12ao...
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A University Algebra

Edward Olney - Algebra - 1880 - 354 pages
...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 equal...square of the first, minus twice the product of the two, plus the square of the second. 87. THEO. — The product of the sum and difference of two quantities...
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Ray's New Higher Arithmetic: A Revised Edition of the Higher Arithmetic

Joseph Ray - Arithmetic - 1880 - 420 pages
...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 equals 25. 8. ()5 equals MrlJ. 2. 14s 2744. 9. (.02) s...
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