 | Stephen Chase - Algebra - 1849 - 348 pages
...similar expressions for the square of any polynomial. Thus, (o+ft+c+z) 2 = (a+b+c) 2+2(a+J+c)z+z2. Hence, The square of any polynomial is equal to the sum of the t quares of the terms, plus twice the sum of their products, taken two and two. § 1 69. (a+x) s =... | |
 | Joseph Ficklin - Algebra - 1874 - 446 pages
...a + Ъ. Сок. 2. — It may be shown by actual multiplication, that and Hence, we may infer that The square of any polynomial is equal to the sum of the squares of its terms, together with twice the sum of the products obtained by multiplying each term... | |
 | American Institute of Electrical Engineers - Electric engineering - 1892 - 888 pages
...(&,«• *+«,)+/ "sin fao <+«.,)+/'"etc.~ t. (186) F0 = /0'sin(i1wi!+W1)4-yo"sin(^+#!i)+/0'"etc. d t. Since the square of any polynomial is equal to the sum of the squares of each term separately plus twice the product of each term by every other term, we have as... | |
 | John Kelley Ellwood - Algebra - 1892 - 312 pages
...claim anything original in its use, it being merely an application of the well.known principle that the square of any polynomial is equal to the sum of the squares of its several terms, plus twice the product of every two terms of the polynomial. For example... | |
 | James Morford Taylor - Algebra - 1893 - 362 pages
...theorem. Thus (3ж + 5»)2=(3a0 = 9ж2 + 25 y1 + З0xy. . Also, (2x-3г/)2=(2ж)2+(-3у)2 - 12 xy. 112. The Square of any Polynomial is equal to the sum of the squares of its several terms plus twice the product of each term into each of the terms that follow... | |
 | Scoby McCurdy - Algebra - 1907 - 264 pages
...— L 14. ж4 — 2 ж2у2 + у4. 17. ж8 — у8. 15. ж-4-?/4. 18. у8 -390625. Page 16, § 52. 1. The square of any polynomial is equal to the sum of the squares of each of its terms, plus twice the product of each term and each of the following terms.... | |
 | George W. Evans - Algebra - 1899 - 456 pages
...the square of the first number, minus twice the product of the two, plus the square of the second. 3. The square of any polynomial is equal to the sum of the squares of the separate terms, added to twice their products, taken two at a time. (The straight products... | |
 | James Morford Taylor - Algebra - 1900 - 504 pages
...63+/ + 2a6 + 2o/ + 26/. (2) And so on for a polynomial of any number of terms. Hence we infer that The square of any polynomial is equal to the sum of the squares of its several terms, plus the sum of the products of twice each term into each of the terms... | |
 | Louis Parker Jocelyn - Algebra - 1902 - 460 pages
...+ 1) (^ + 1) (У + 1). 12. (а + Ь) (а2 - ab + Ь'2) (а - ¿>) (а2 + ab + b1). 171. Theorem 6. The square of any polynomial is equal to the sum of the squares of the several terms, plus the sum of twice the products of each term by each term that follows... | |
 | Henry Burchard Fine - Algebra - 1904 - 612 pages
...6)8 + 3 (a + 6)2c + 3 (a + 6) c2 + c8 Generalixing the first of these results we have the theorem : The square of any polynomial is equal to the sum of the 316 squares of all its terms together with twice the products of every two of its terms. Example 1.... | |
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Since the square of any polynomial is equal to the sum of the squares of each term separately plus twice the product of each term by every other term... 
