 | 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;«.... | |
 | 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... | |
 | Bourdon (M., Louis Pierre Marie) - Algebra - 1850 - 386 pages
...square of the ßrst, minus twice the product of the ßrst 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 —... | |
 | 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 —... | |
 | 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*—... | |
 | 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... | |
 | 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... | |
 | 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 - 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... | |
 | 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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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. 
