| 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;«.... | |
| |