The square of the difference of 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. New University Algebra - Page 36by Horatio Nelson Robinson - 1875 - 412 pagesFull view - About this book
| Benjamin Greenleaf - 1863 - 338 pages
...6 -f- 4 a4 6s. . 4. Square a3 V + 3 a2 6s c4. Ans. a" 64 + 6 a5 Jf c4 + 9 a4 6" c8. THEOREM II. 77i The square of the difference of two quantities is...of the first, minus twice the product of the first by the second, plus the square of the second. For, let a represent one of the quantities, and 6 the... | |
| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...second, plus the square of the second. II. (a— b)'=(a— ¿) (a— b)=a'— 2ab+b* Or, in words, The square of the difference of two quantities is equal to the square of the ßrst, minus twice the product of the first and second, plus the square of the second. III. (ti+6)... | |
| Benjamin Greenleaf - Algebra - 1864 - 336 pages
...4 a4 62. 4. Square a5 62 + 3 a2 W c4. Ans. a6 64 4- 6 a" 6" c4 4- 9 a4 66 c8. ' THEOREM II. 77. ^%e square of the difference of two quantities is equal...of the first, minus twice the product of the first ty the second, plus the square of the second. For, let a represent one of the quantities, and b the... | |
| Paul Allen Towne - Algebra - 1865 - 314 pages
...numerical value when a; = 8, y = 8. 63. Since (*— y) ( x -y) = (x — yf = x'-2xy+y3, it follows that The square of the difference of two quantities is equal to the square of the first — twice their product -\- the square of the last. EXAMPLES. 1. (« — 6)" = ^ — 2a6 + 62. 2. (2a... | |
| Joseph Ray - Algebra - 1852 - 422 pages
...proves the theorem AP PL I CAT ION. 1. (2+5)'=4+20+25=49. 2. (2m+ 3. ( 4. ( ART. 79. THEOREM II. — The square of the difference of two quantities is...of the first, minus twice the product of the first by the second, plus the square of the se'vnd. Let a represent one of the quantities, and b the other... | |
| Benjamin Greenleaf - 1866 - 336 pages
...+ 4 a4 ô2. 4. Square a3 b2 + 3 a2 a3 c4. Ans. a6 54 + 6 a5 55 c4 + 9 a4 #> c3. THEOREM II. 77t 7%e square of the difference of two quantities is equal...square of the first, minus twice the product of the firsl by the second, plus the square of the second. For, let a represent one of the quantities, and... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...a&+62 a?— 2a6+62 But a — b is the difference of the quantities, a and' 6. Hence, Theorem II. — The square of the difference of two quantities is equal to the square of the first, minus twice the prodnet of the first by the second, plus the square of the second. 1. (5— 4)2=25— 40+16=1. 2'.... | |
| Joseph Ray - Algebra - 1866 - 250 pages
...a?—ab a2— 2a6-|-62 But a — b is the difference of the quantities, a and 6. Hence, ! Theorem II. — The square of the difference of two quantities is equal to the square of the first, minus twice the prodvet of the first by the second, phis the square of the second. 1. (5— 4)2=25— 40+16=1. 2. (2a—... | |
| Charles Davies - Algebra - 1866 - 314 pages
...(a - b) (a- b) = a2- 2ab + P. That is, The square of the difference of any two quantities is eq^^al to the square of the first, minus twice the product of the first by the second, plus the square of the second. 1. Find the square of 2a — b. We have, (2a — b)2... | |
| Horatio Nelson Robinson - 1868 - 430 pages
...second, plus the square of the second. II. (a— l)'=(a— ¿) (a— i) = a'— ïab+V Or, in words, The square of the difference of two quantities is...first, minus twice the product of the first and second, phis the square of the second. III. (a+l) (a_b)=a«_ £,' Or, in words, The product of the sum and... | |
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