| Algebra - 1848 - 368 pages
...the following theorems. THEOREM I. The square of the sum of two quantities is equal to the squarg vf **the first, plus twice the product of the first by the second,** plut the square of the second. Let a denote one of the quantities and b the other : then a + Ъ = their... | |
| Charles Davies - Algebra - 1850 - 292 pages
...the square or second power of the binomial (a-{-b). We have, from known principles, 2=(a+ b) (a+b)=a* **That is, the square of the sum of two quantities is...plus the square of the second. 1. Form the square of** 2a-\-3b. We have from the rule (2a +36)2 — 4a2 + I2ab -f 962. 2. (5ab +3«c)2 = 3. (5a2+8a26)2 4.... | |
| Charles Davies - Algebra - 1851 - 300 pages
...frequent use in Algebra. Let it be required to form the square or second power of the binomial (a+6). **We have, from known principles, ' That is, the square...plus the square of the second. 1. Form the square of** 2a+3b. We have from the rule (2a + 36)2 = 4a2 + 12a6 + 962. 2. (5a6+3ac)2 = 25a262 + 30a26c+ 9a2e2.... | |
| Joseph Ray - Algebra - 1852 - 410 pages
...following theorems, which may be regarded as the simplest application of Algebra. ART. 78. THEOREM I. — **The square of the sum of two quantities is equal to...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 sum ; and (a+6)X(a+*)> or (<z+6)'=the... | |
| Joseph Ray - Algebra - 1848 - 248 pages
...product will be o2+2a6+62 ; thus : a+b But a-\-b is the sum of the quantities, a and b : hence THEOREM I. **The square of the sum of two quantities, is equal...twice the product of the first by the second, plus** thz square of the second. EXAMPLES. NOTE. — The instructor should read each of the following examples... | |
| New York (State) School for the deaf, White Plains - 1854 - 936 pages
...gives minus." (b-— 1)=! (If— 1)=(&6— &s)." What is the square of the sum of two quantities T " **The square of the sum of two quantities is equal to...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
...Required the square of 3+2 v/5. These two examples are comprehended under the rule in Art. 60, that **the square of the sum of two quantities is equal to...first by the second, plus the square of the second.** Ex. 3. Required the cube of ^/x+3^/y. Ex. 4. Required the fourth power of v/3— ^2. Ans. 49— 20V"?.... | |
| Dana Pond Colburn - Arithmetic - 1855 - 396 pages
...the second, and b2 equals the 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 +... | |
| Thomas Sherwin - Algebra - 1855 - 264 pages
...Hence the second power of the sum of two quantities contains the second power of the first quantity, **plus twice the product of the first by the second, plus the** second power of the second. Find the second power of a — 6. Operation. a — 6 a — 6 • a2 —... | |
| Dana Pond Colburn - Arithmetic - 1856 - 392 pages
...the second, and b2 equals the 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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