 | 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... | |
 | 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 - 462 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 of their squares. EXAMPLES Expand by inspection : 1. (x + y) (x - y). 6. (r + s)(r-8). 2. (a + c)(a— c). 7. (x + 1)... | |
 | 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.... | |
 | Robert Gordon Blaine - Slide-rule - 1903 - 178 pages
...one less than the number of integer figures in the number it represents. DIFFERENCE OF TWO SQUARES. The product of the sum and difference of two numbers is equal to the difference of their squares. This rule is often useful in using the slide-rule so as to enable us to turn the difference of two... | |
 | John Marvin Colaw - Algebra - 1903 - 444 pages
...62, III. The product of the sum and difference of two numbers. By multiplication, we have That is, the product of the sum and difference of two numbers is equal to the difference of their squares. Thus, (5 + 3) (5 - 3) = 25 -0 = 16; IV. The cube of the sum of two numbers. % By multiplication we... | |
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Thus the product of the sum and difference of two numbers is equal to the difference of their squares. 
