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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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Elements of Algebra: For Colleges, Schools, and Private Students, Book 2

Joseph Ray - Algebra - 1866 - 420 pages
...theorem. APPLICATION. 1. (2+5)2=4+20+25=49. 3. (ax+by)*=ax* -\-2abxy -\-by*. 4. ' 79. Theorem II. — The square of the difference of two quantities is equal...of the first, minus twice the product of the first ly the second, plus the square of the second. Let a represent one of the quantities, and 6 a — 6...
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New Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1866 - 316 pages
...(a - b) (a- b) = a2- 2ab + P. That is, The square of the difference of any two quantities is eq^^al to the square of the first, minus twice the product...first by the second, plus the square of the second. 1. Find the square of 2a — b. We have, (2a — b)2 = 4a2 — 4ab + b2. 2. Find the square of 4ac...
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New Elementary Algebra

Benjamin Greenleaf - 1866 - 338 pages
...+ 4 a4 2. 4. Square a3 b2 + 3 a2 a3 c4. Ans. a6 54 + 6 a5 55 c4 + 9 a4 #> c3. THEOREM II. 77t 7%e square of the difference of two quantities is equal...square of the first, minus twice the product of the firsl by the second, plus the square of the second. For, let a represent one of the quantities, and...
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Ray's Algebra, First Book: Primary Elements of Algebra, for Common Schools ...

Joseph Ray - Algebra - 1866 - 252 pages
...a?— 2a6+62 But a — b is the difference of the quantities, a and' 6. Hence, Theorem II. — The 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'....
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Primary Elements of Algebra: For Common Schools and Academies

Joseph Ray - Algebra - 1866 - 252 pages
...a2— 2a6-|-62 But a — b is the difference of the quantities, a and 6. Hence, ! Theorem II. — The square of the difference of two quantities is equal to the square of the first, minus twice the prodvet of the first by the second, phis the square of the second. 1. (5— 4)2=25— 40+16=1. 2. (2a—...
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New Elementary Algebra

Benjamin Greenleaf - 1867 - 336 pages
...a; y -\- y3. 3. Square 6 a2 -f- 2 a2 b. Ans. 4. Square o3 62 + 3 a> 6s c4. Ans. THEOREM II. 77i y^ square of the difference of two quantities is equal...represent one of the quantities, and b the other; then, (o — 6)' = (a — J) X (a — 6) = ' — 2 a 6 + 6', which proves the theorem. EXAMPLES. 1. Find...
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Elementary Algebra

Charles Davies - Algebra - 1867 - 320 pages
...(a — 6)2 = (a — 6) (a — 6) = a2 — 2a6 + 62 : Thaf. is, The square of the difference between two quantities is equal to the square of the first, minus twice the product of the first by 1h* second, plus the square of the second. 1. Form the square of 2a — b. We have (2o- 6)2 = 4a2 -...
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A Treatise on Algebra

Elias Loomis - Algebra - 1868 - 386 pages
...(5a+3Z>) 2 = 8. 4. (5a 2 +2&) 2 ^ 9. 5. (5a*+b) 2 = 10. 67. The square of the difference of two numbers is equal to the square of the first, minus twice 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....
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New University Algebra: A Theoretical and Practical Treatise Containing Many ...

Horatio Nelson Robinson - 1868 - 430 pages
...second, plus the square of the second. II. (a— l)'=(a— ) (a— i) = a'— ab+V Or, in words, The square of the difference of two quantities is equal...of the first, minus twice the product of the first and second, phis the square of the second. III. (a+l) (a_b)=a_ ,' Or, in words, The product of...
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Eaton's Elementary Algebra: Designed for the Use of High Schools and Academies

William Frothingham Bradbury - Algebra - 1868 - 264 pages
...y2. 2. 2x + 2y. Ans. 4 a;2 3. x+ 1. 4. 4 + a;. 5. 2x + 3y. Ans. 4z2-f6. 3a + 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 a and 6 represent the two quantities, and a ]> 6 ; their difference...
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