| 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 - 302 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 - 408 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 - 250 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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