 | Algebra - 1848 - 394 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 - 408 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 - 250 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 - 262 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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That is, 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. 
