 | Charles Davies - Algebra - 1842 - 368 pages
...power of the binomial, (a-\-b). We have, from known principles, (a + b)2=(a+b) (a+i)=a 2 +2ai+i 2 . That is, the square of the sum of two quantities is...first by the second, plus the square of the second. Thus, to form the square of 5o 2 +8a 2 i, we have, from what has just been said, (5a 2 + 8a 2 i) 2... | |
 | Ormsby MacKnight Mitchel - Algebra - 1845 - 294 pages
...14a26c5+14a62c5— 3a2ce— 7 16. Multiply a+6 by a+b. The product is a2+2a6-}-62; from which it appears, that the square of the sum of two quantities, is equal...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 the square... | |
 | Charles Davies - Algebra - 1845 - 368 pages
...the multiplication of algebraic quantities in the demonstration of the following theorems. 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 denote one of the quantities and l1 the other: then a + b — their sum. Now, we have from known... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...Required the square of 3 + 2 \/ 5. These two examples are comprehended under the rule in Art. 60, that the square of the sum of two quantities, is equal...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. • ÇA... | |
 | Elias Loomis - Algebra - 1846 - 346 pages
...Theorems are of such extensive application that they should be carefully committed to memory. THEOREM I. The square of the sum of two quantities is equal to...first by the second, plus the square of the second. Thus if we multiply a + b By a + b a2 + ab ab+b2 We obtain the product n2 + 2ab + Thus if we wish to... | |
 | Algebra - 1847 - 368 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, we have... | |
 | Charles Davies - Algebra - 1848 - 279 pages
...reference to algebraic multiplication, we will make known a few results of frequent use in Algebra. I ,et it be required to form the square or second power...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 =25a2i2+ 30a2ic+ 9a2c2. 3.... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...be a2+2a6+62; thus: a+6 a+6 a2+a6 But a-\-b IB the sum of the quantities, a and 6 ; hence THEOREM I. The square of the sum of two quantities, is equal...first by the second, plus the square of the second. EXAMPLES. NOTE. — The instructor should read each of the following examples aloud, and require the... | |
 | 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 + 3ac)2 =25a2i2+ 30a2ic+ 9a2c2.... | |
 | 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— 2axs+a;«.... | |
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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. 
