 | George Peacock - 1830 - 732 σελίδες
...other. This is the square of a + b (Art. 11), and the result may be expressed in words, as follows : " The square of the sum of two quantities is equal to the sum of the squares of the two quantities, together with twice their product.1"* (2) To find the square... | |
 | Charles Davies - 1835 - 378 σελίδες
...principles, (a+by=(a+b) (a+b)=a3+'2ab+b3. That is, the square of the sum of two quantities is composed of the square of the first, plus twice the product of the first by the second, plus the square of the second. Thus, to form the square of 5a3+8a3i, we have, from what has just been... | |
 | Silas Totten - 1836 - 320 σελίδες
...4a6a) x (7asb + 4a62) = 49a«6s — 16а»ЬЧ The following properties are also of great use : — 1. The square of the sum of two quantities, is equal to the sum of their squares plus twice their product. Let a and b be the quantities, then a -fb is theipsum,... | |
 | Charles Frederick Partington - 1838 - 1116 σελίδες
...will be useful exercises. It is required to prove 1°. That (a + 6) (n + b) = os + lab + 63 ; or, that the square of the sum of two quantities is equal to the square of the first quantity, plus the square of the second, plus twice the product of the first and second. 2°. That... | |
 | Charles Davies - 1839 - 264 σελίδες
...required to form the square or second power of the binomiaj (a+b). We have, from known principles, That is, the square of the sum of two quantities is...plus twice the product of the first by the second, plus the square of the second. 1. Form the square of 2a+36. We have from the rule (2a + 36)2 = 4<z3... | |
 | Charles Davies - 1840 - 264 σελίδες
...required to form the square or second power of the binomial (a+6). We have, from known principles, That is, the square of the sum of two quantities is...square of the first, plus twice the product of the frst by the second, plus the square of the second. 1. Form the square of 2a+3J. We have from the rule... | |
 | Charles Davies - 1842 - 368 σελίδες
...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...plus twice the product of the 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... | |
 | Charles Davies - 1842 - 284 σελίδες
...required to form the square or second power of the binomial (a-\-b). We have, from known principles, That is, the square of the sum of two quantities is...plus twice the product of the first by the second, plus the square of the second. 1. Form the square of 2a+36. We have from the rule (2a + 36)2 = 4a2... | |
 | Ormsby MacKnight Mitchel - 1845 - 308 σελίδες
...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...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... | |
 | Charles Davies - 1845 - 382 σελίδες
...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...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 —... | |
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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. 
