 | Education - 1900 - 804 pages
...squares of the other two sides; I can not recall that I ever gave out from the pulpit as a text, that the product of the sum and difference of two numbers is equal to the difference of their squares. But I remember that, when, a boy about 14 years of age, I sat in my room all alone and worked it out... | |
 | George W. Evans - Algebra - 1899 - 456 pages
...other; that is, showing the equation to be identical. 108. Model A. — Prove the following theorem: The product of the sum and difference of two numbers is equal to the difference of their squares. * Proof. — Let a and b represent any two numbers, then the theorem is expressed by the following... | |
 | Frank Castle - Mathematics - 1899 - 424 pages
...odd number. a" — b° ,, ,, ab ,, is odd. a" — 6° „ „ both a + b and a - b when n is even. The product of the sum and difference of two numbers is equal to the difference of their squares. CHAPTER VII MEASURES AND MULTIPLES. HCF AND LCM FRACTIONS. WE have already found that and by multiplying... | |
 | Frank Castle - Mathematics - 1900 - 200 pages
...is an odd number. a" --" „ ,, a- b ,, is odd. a" - b" , , , , both a + b and a - b when n is even. The product of the sum and difference of two numbers is equal to the difference of their squares. CHAPTER XIV. APPROXIMATIONS. FRACTIONS. WE have already found that and by multiplying again by a +... | |
 | John Marvin Colaw, John Kelley Elkwood - Arithmetic - 1900 - 450 pages
...the difference of two numbers is equal to what ? 39. Multiply x + y by x — y, and note the product. The product of the sum and difference of two numbers is equal to the difference of what ? Write the products of the following : 40. (c + d) (c + d). 43. (3y - 5) (3y - 5). 41. (c + d)... | |
 | William James Milne - Algebra - 1901 - 476 pages
...terms of the product obtained from the numbers ? 3. What sign connects the squares ? 97. PRINCIPLE. — The product of the sum and difference of two numbers is equal to the difference oftheir squares. EXAMPLES Expand by inspection : 1. (x + y) (x — y). 6. (r + s)(r — s). 2. (a +... | |
 | James Harrington Boyd - Algebra - 1901 - 818 pages
...their product. Finally III. (<i + b) (a — b) = «* — b*. Thus, the product of t/te sum and the difference of two numbers is equal to the difference of their squares. 87. The Double Sign — The sign ± is sometimes used, and is called the double sign. Since (а+Ь)*=аа+2п/>... | |
 | William James Milne - Algebra - 1902 - 620 pages
...by multiplying it by some factor that will give the square of each term, but no other terms. Since the product of the sum and difference of two numbers is equal to the difference of their squares, the simplest rationalizing factor for V5 + V3 is its conjugate, V6 — V3 (Prin.). 12. Find the simplest... | |
 | Alvord D. Robinson - Arithmetic - 1902 - 572 pages
...two numbers. ab a + b a2 - ab + ab-b* a2 -b3 From the work, the following principle is derived: — The product of the sum and difference of two numbers is equal to the square of the first minus the square of the second. For the Pupil : 1. State the 3 principles of multiplication.... | |
 | George Albert Wentworth - Algebra - 1903 - 344 pages
...equal to the sum of their squares — twice their product. From (3) we have (a + é) (a — b) = a* — b*. That is, 76. The product of the sum and difference...numbers is equal to the difference of their squares. (1) a 4 a -\ аЧ - Ь ( - Ь - ab ab + b2 2) a — Ь ( а— Ь a* — ab — ab + b* [S) a+ Ь a... | |
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The product of the sum and difference of two numbers is equal to the difference of their squares. 
