 ... the 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 to the square of the first, minus twice the product of the first by the second, plus the square...  Elementary Algebra Revised - Page 89by Frederick Howland Somerville - 1913 - 447 pagesFull view - About this book
 | Joseph Ray - Algebra - 1852 - 408 pages
...4. (ax2+3;i:z3)2 ART. 79. THEOREM II. — The square of the difference of two quantities is equal to the square of the first, minus twice the product of...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 —... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...quantities a and b ; hence THEOREM II. 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 tecond, plus the sqitare of the second. EXAMPLES. 1. (5-4)*=25-40+16=l. 2. (2a— 6)2=4a2 3. (3*—... | |
 | 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... | |
 | 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 +... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...of a+b equal to a'+b'. THEOREM II. (61.) The square of the difference of 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. Thus, if we multiply a — b By a- b a'- ab - ab+b' lVe... | |
 | 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... | |
 | Elias Loomis - Algebra - 1856 - 280 pages
...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 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... | |
 | Joseph Ray - Algebra - 1857 - 408 pages
...78. THEOREM I. — 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. Let a represent one of the quantities, and b the other ; then a+J=their sum ; and (a+6)X (o+J), or... | |
 | Charles Davies - Algebra - 1857 - 408 pages
...— b)2 = o2 - 2ab + b2 ; that 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 Iht second, plus the square of the second. To apply this to an example, we have (7a2J2 _ 12a63)2 =... | |
 | Silas Lawrence Loomis - Arithmetic - 1859 - 324 pages
...before proceeding further. 357. PRIN. 3. — THE SQUARE OF THE DIFFERENCE OF TWO NUMBERS, IS EQUAL TO THE SQUARE OF THE FIRST, MINUS TWICE THE PRODUCT OF...FIRST BY THE SECOND, PLUS THE SQUARE OF THE SECOND. ILLUSTRATION 1 . — Required the square of 27 27 = 30 _ 3. The square of 27 then is 900 — 2 x 90... | |
| |
