 | Charles Davies - Algebra - 1845 - 382 pages
...demonstration of the following theorems. 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 denote one of the quantities and l1 the other: then a + b — their sum. Now, we have... | |
 | Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...product is a2+2a6-}-62; from which it appears, that 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. 17. Multiply a — b by a — b. The product is a2 — 2a6+62 ; from which we perceive, that... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...are comprehended under the rule in Art. 60, that 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. Ex. 3. Reqired the cube of \/ x + 3 \/ y. Ex. 4. Required the fourth power of v/ 3 — \/ 2.... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...are comprehended under the rule in Art. 60, that 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. Ex. 3. Reqired the cube of \/ x + 3 V y. Ex. 4. Required the fourth power of V 3 — \/ 2.... | |
 | Algebra - 1847 - 408 pages
...II. The square of the difference between 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. Let a represent one of the quantities and b the other : then a — b = their difference. Now,... | |
 | Charles Davies - Algebra - 1848 - 302 pages
...(a-\-b). We have, from known principles, 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. 1. Form the square of 2a+3b. We have from the rule (2a +3i)2 =: 4a2 + 12ai + 9i2. 2. (5ai+3ac)2... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...of the quantities, a and 6 ; hence 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. EXAMPLES. NOTE. — The instructor should read each of the following examples aloud, and require... | |
 | Charles Davies - Algebra - 1848 - 300 pages
...known principles, That is, the square of the sum of two quantities is equal to the square of the jlrst, plus twice the product of the first by the second, plus the square of the- second. 1. Form the square of 2<z+3i. We have from the rule (2a + 3i)2 = 4a2 + I2ab + 9i2. 2. (5ai... | |
 | Joseph Ray - Algebra - 1848 - 252 pages
...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—... | |
 | 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... | |
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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. 
