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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 University Algebra

Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...second, plus the square of the second. II. (a — b)*=(a—b)(a — b) = a*—2ab + & ; hence, The square of the difference of two quantities is equal...of the first, minus twice the product of the first and second, plus the square of the second. III. (a +b)(a — b)—a*-^; hence, Tue product of the sum...
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Manual of Algebra

William Guy Peck - Algebra - 1875 - 348 pages
....product of the first and second, plus the square of the second. 2░. The square of the difference of any two quantities, is equal to the square of the first, minus twice the product of the first and second, plus the square of the second. 3░. The product of the sum and difference of any two quantities,...
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A Practical Business Arithmetic ...

Lorenzo Fairbanks - 1875 - 468 pages
...is a quantity consisting of two terms, and its square is equal to the square of the first term, plus twice the product of the first by the second, plus the square of the second. Let 35 be written 30 + 5. Then, squaring this number, by multiplying each part separately, we hare,...
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A school algebra to quadratic equations

Charles Mansford - 1875 - 110 pages
...square of the first + twice the product of two quantities + the square of the second. And from (ii.) The square of the difference of two quantities is equal to the square of the first — twice the product of the quantities + the square of the second. Twice Sq. of Sq. of first. the...
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New Elementary Algebra

Benjamin Greenleaf - 1876 - 334 pages
...36a4-f-24a4╗ + 4a4i2. 4. Square o? & + 3 a2 63 c4. Ans. a6 64 + 6 a5 i5 c4 -f- 9 a4 If c3. THEOREM II. 77, The square of the difference of two quantities is equal...second, plus the square of the second. For, let a repreient one of the quantities, and b the other; then, (a — 6)2 = (a — 6) X (a — 6) = a2 —...
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New Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1876 - 324 pages
...we have, (a - o)2 = (a - &) (a - o) = a2 - 2ao + ˇ2. That is, 7%e square of (he difference of any two quantities is equal to the square of the first, minus twice the product of the▀rst by the second, plus the square of the second. 1. Find the square of 2a — b. We have, (2a...
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Bradbury's Elementary Algebra: Designed for the Use of High Schools and ...

William Frothingham Bradbury - Algebra - 1877 - 280 pages
...4x2+ 8x 3. a; + 1. 4. 4 + *. 5. 2x + 3y. Ans. 4 *2 4-1? xy + 9 /. 6. Зa + 6. THEOREM III. 59. 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. Let о and b represent the two quantities, and a ]> b ; their dii...
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The Complete Algebra: Embracing Simple and Quadratic Equations, Proportion ...

Edward Olney - Algebra - 1877 - 468 pages
...За*Ь'-. Result, 25а - " + ЗОаб╗ + б. Square $a÷-ź + $a:-'b-'. ▀esult, 93, THEO. — Tlœ square of the difference of two quantities is equal to the square of the ▀rst, minus twice the product ofthe▀rut by tlie second, plus Die square of the second. DEM. — Let...
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New Elementary Algebra: In which the First Principles of Analysis are ...

Benjamin Greenleaf - Algebra - 1877 - 662 pages
...quantities is equal to the square of the first, plus 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, (ź + i)' = (a -f- 1) x (a + b) = a2 + 2 ai + V. Hence, the theorem is true. •...
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A University Algebra

Edward Olney - 1878 - 362 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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