 | William James Milne - Algebra - 1908 - 476 pages
...+ b their sum, and a — b their difference. Show by actual multiplication that 114. PRINCIPLE. — The product of the sum and difference of two numbers is equal to the difference of their squares. EXERCISES 115. Expand by inspection, and test each result : 1. (x + y)(xy). 11. (a6 + 5)(a6-5). 2.... | |
 | Robert Louis Short, William Harris Elson - Mathematics - 1910 - 200 pages
...multiplication : a + b 0-6 - ab - b2 a? -b2 That is, (a + ft)(a - &) = a2 - &2. Or, stated in words : The product of the sum and difference of two numbers is equal to the difference of their squares. Then to multiply the sum of two numbers, as 3 x + 5, by the difference of the same two numbers, 3 x... | |
 | Arthur Schultze - Algebra - 1918 - 336 pages
...product of the first and the second, plus the, square of the second. III. The product of the sum and the difference of two numbers is equal to the difference of their squares. The student should note that the second type (II) is only a special case of the first (I). Ex. (4 ¡e8... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...numbers is equal to the sum of their squares plus twice their product. The product of the sum and the difference of two numbers is equal to the difference of their squares. GEOMETRIC THEOREMS. The square on the sum of two lines is equal to the sum of the squares on the lines... | |
 | William James Milne - 1911 - 360 pages
...difference of two numbers obtained from the numbers ? 3. What sign connects the terms ? 94. PRINCIPLE. — The product of the sum and difference of two numbers is equal to the difference of their squares. EXERCISES 95. Expand by inspection, and test each result : 1. (x + y)(xy). 16. (2x + 3y)(2x-3y). 2.... | |
 | Gustavus Sylvester Kimball - Business mathematics - 1911 - 444 pages
...case involve the principles 32= o, of the well-known theorem that, "The product of the sum and 515~ difference of two numbers is equal to the difference of their squares. " Half the sum of 22 and 28 is 25. Square 25 and we have 625. The difference between 28 and 22 is 6,... | |
 | Methodist Church - 1845 - 664 pages
...extreme, presenting throughout the matter, and nowhere separately, the form, which is like proving that the product of the sum and difference of two numbers is equal to the difference of their squares, not by writing a + b Xa — b = a* — b*', but thus: 5 and 3 are 8, 3 from 5 leave 2, twice 8 is 16... | |
 | John William Hopkins, Patrick Healy Underwood - Algebra - 1912 - 362 pages
...The required product is the différât2 + ab ence between a(a + 6) and b(a + b). -ab-b* a2 -62 Hence, The product of the sum and difference of two numbers is equal to the difference of the squares of the numbers. (Ill) Geometric Proof. Let AB = a, BC=b. Upon AB describe the square ABKE,... | |
 | William James Milne - Algebra - 1914 - 514 pages
...multiplication that Also that 32 x 28 = (30 + 2) (30 - 2) = 302 - 2* = 896. 114. PRINCIPLE. — Tlie product of the sum and difference of two numbers is equal to the difference of their squares. EXERCISES [Additional exercises are given on page 465.] 115. Expand by inspection, and test each result... | |
 | George Howe - Mathematics - 1915 - 168 pages
...product of the sum and difference of two terms such as (a + 6) X (a — b) equals a2 — 5*; or, briefly, the product of the sum and difference of two numbers is equal to the difference of their squares. By trial it is often easy to discover the factors of algebraic expressions; for example, 2в* + 7а6... | |
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The product of the sum and difference of two numbers is equal to the difference of their squares. 
