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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

The Elements of Algebra

Elias Loomis - Algebra - 1868 - 312 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 to the square of the first, minus twice theprod~ net of the first and second, plus the square of the second. Thus, if we multiply a —b by...

Elements of algebra

Robert Wallace - 1870 - 164 pages
...Iheorem for finding the square of the difference of any two quantities is deduced. THEOREM II. — The square of the difference of two quantities is equal...first by the second, plus the square of the second. EXAMPLES. 1. 2. 3. 4. 5. **. 'J — ~4f — "g Y~TTn — r44 x — y)2=(x — y] (xy)=x2 — 2xy-\-y-....

Elements of Algebra: For Colleges, Schools and Private Students

Joseph Ray - Algebra - 1866 - 420 pages
...the theorem. APPLICATION. 1. (2+5)2=4+20+25=49. 2. (2m+3n)2=4m2-f I2wm+9n2. 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 6 a — 6 the other. a — b Then, a — 6= their difference;...

New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - Algebra - 1871 - 412 pages
...square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (2) That is, The square of the difference of two quantities is equal...first by the second, plus the square of the second. Also, (a _|- 5) (a — 5) = a2 — 52. (3) That is, jTAe product of the sum and difference of two quantities...

An Elementary Algebra for Schools and Academies

Joseph W. Wilson - Algebra - 1873 - 268 pages
...a fl2 , ^~ + b by itself, we have what the theorem ' ab + V states. as + 2 ab + b2 Theorem II. 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. a — b PROOF. Let a and b stand for any a — b two quantities....

A University Algebra ...

Edward Olney - Algebra - 1873 - 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...

The Art of Computation, Designed to Teach Practical Methods of Reckoning ...

David White Goodrich - Ready-reckoners - 1873 - 220 pages
...3969, etc. Again, since (a— by=a' — 2«5-t-6", the square of the difference of two numbers equals the square of the first, minus twice the product of...first by the second, plus the square of the second. Thus 19" = 400—40+2 = 361. 95" = 10000—1000+25 = 9025. 85'= 8100— 900+25 = 7225. 57"= 3600- 360+...

A Treatise on Algebra

Elias Loomis - Algebra - 1873 - 396 pages
...(5a3+8a26)2= 3. (5a+36)2= 8. 4. (5a2+ 26)2= 9. 5. 5a3+i= 10. 67. T/ie square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the sec~ and, plus the square of the second. Thus, if we multiply a— 6 by a— b a?— ab - ab+bz we...