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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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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 252 pages
...quantities a and b; hence THEOREM II. The square of the difference of two quantities, is equal to {he square of the first, minus twice the product of the...first by the second, plus the square of the second. EXAMPLES. 1. (5-4)2=25-40+16=l. 2. (2a— 6)2=4a2 3. (3x-2y)2 4. (al-yI)╗=z 5. (ax— x*Y=aW— 2axs+a;ź....
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1848 - 279 pages
...39. To form the square of a difference a — b, we have That is, the square of the difference between two quantities is equal to the square of the first, minus twice the product of the Jirst by the second, plus the square of the second. 1. Form the square of 2a — b. We have 2. Form...
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Elements of Algebra: Including Sturms' Theorem

Bourdon (M., Louis Pierre Marie) - Algebra - 1850 - 386 pages
...square of the ▀rst, minus twice the product of the ▀rst by tht second, plus Ihe square of the second. Let a represent one of the quantities and b the other : then а — b = their difference. Now, we have from known principles, (a — ┐)2 = (a — ┐) X (a —...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - Algebra - 1852 - 410 pages
...(2+5)2=4+20+25=49. ALGEBRAIC THEOREMS. 3 . (oa+iy) 2=aV+2 abxy+tfy*. 4. (ax2+3;i:z3)2 ART. 79. THEOREM II. — The square of the difference of two quantities is equal...first by the second, plus the square of the second. Let a represent one of the quantities, and b the other ; then a — i=their difference ; and (a —...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 248 pages
...6 a2 — a6 — ab+V But a—b is the difference of tho quantities a and b ; hence THEOREM II. The square of the difference of two quantities, is equal...first, minus twice the product of the first by the tecond, plus the sqitare of the second. EXAMPLES. 1. (5-4)*=25-40+16=l. 2. (2a— 6)2=4a2 3. (3*—...
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Annual Report and Documents, Volumes 35-42

New York (State) School for the deaf, White Plains - 1854 - 936 pages
...two quantities T " 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." (la— 5Z>)S= what! " (la— 5Z>)3= 49as— 70ab+25b\" Resolve a2 — b~ into factors 1 What is the...
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A Treatise on Algebra

Elias Loomis - Algebra - 1855 - 356 pages
...most common mistakes of beginners is to call the square of a+b equal to a'+b'. THEOREM II. (61.) 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. Thus, if we multiply a — b By a- b a'- ab - ab+b' lVe...
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - Arithmetic - 1855 - 396 pages
...square of the second ; The square of the sum of any two numbers equals the square of the first, plus twice the product of the first by the second, plus the square of the tecond. Illustrations. (7 + 5)2 = 72 + 2 X 7 X 5 + 52 = 49 + 70 + 25 = 144 = 122 (8 -f- 4)a = 82 +...
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The Elements of Algebra

Elias Loomis - Algebra - 1856 - 280 pages
...most common mistakes of beginners is to call the square of a+b equal to a'+b\ THEOREM II. (66.) 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. Thus, if we multiply a —b by a —b a'- ab - ab+b' we...
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - Arithmetic - 1856 - 392 pages
...square of the second ; The square of the sum of any two numbers equals the square of the first, plus twice the product of the first by the second, plus the square of the tecond. Illustrations. (7 + 5)2 = 72 + 2 X 7 X 5 + S2 = 49 + 70 + 25 = 144 = 12╗ (8 + 4)2 = 82 + 2...
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