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" RULE 3. The product of the sum and difference of two numbers is the difference of their squares. "
The First Steps in Algebra - Page 65
by George Albert Wentworth - 1894 - 184 pages
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The Elements of Algebra: Designed for Beginners

Elias Loomis - Algebra - 1868 - 312 pages
...of 1 1 to 13, and the sum of their squares is 14,210. What are the numbers ? Ans. 77 and 91. Prob. 3. The product of the sum and difference of two numbers is 176, and the sum of the numbers is to their difference as 11 to 4. What are the numbers? Ans. 15 and...
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Elementary algebra, with brief notices of its history

Robert Potts - 1879 - 668 pages
...any two numbers, is equal to the difference between tho sum of their squares and twice their product. (3) The product of the sum and difference of two numbers, is equal to the difference of the squares of the two numbers. (See Eue. ii. 5. Cor.) And the first and...
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Elementary algebra: with brief notices of its history

Robert Potts - Algebra - 1879 - 672 pages
...any two numbers, is equal to the difference between the sum of their squares and twice their product. (3) The product of the sum and difference of two numbers, is equal to the difference of the squares of the two numbers. (See Eue. ii. 6. Cor.) And the first and...
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A School Algebra

George Albert Wentworth - Algebra - 1891 - 380 pages
...Difference of Two Numbers. (a + b) (a - b) = a (a - b) + b (a - b) = a2 — ab + ab — V = a2 - b\ Hence, we have RULE 3. The product of the sum and...If we put 2x for a and 3 for b, we have Rule 1, (2x + 3)2 = 4ж2 + l2 x + 9. Rule 2, (2ж-3)2 = 4^- 12ж + 9. Rule3, (2 Exercise 19. Write the product...
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A School Algebra

George Albert Wentworth - Algebra - 1891 - 380 pages
...b)(ab) = a(ab) + b(a- ¿) = a' — ab + ab — V = a2 - b\ Hence, we have RULE 3. The product of ike sum and difference of two numbers is the difference...squares. If we put 2x for a and 3 for b, we have Rule 1, (2х+3)2 = 4з?+12х + 9. Rule 2, (2a;-3)2 = 4^-12a; + 9. Rule3, (2г + 3)(2г-3)=4^-9. Exercise 19....
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A Higher Algebra

George Albert Wentworth - Algebra - 1891 - 544 pages
...Difference of Two Numbers. (a + ¿)0 — è) = a (a — è) + b (a — ¿) = a2 — ab + ab — W = a2 - V. Hence we have RULE 3. The product of the sum and difference...of two numbers is the difference of their squares. 82. Illustrations. If we put 2 x for a and 3 for b, we have Rule 1, (2ж + 3)2 = 4ж2+12a; + 9. Rule...
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A School Algebra

George Albert Wentworth - Algebra - 1893 - 370 pages
...— ah — ab + V Hence we have 101. Product of the Sum and Difference of Two Numbers. ab-V = a2 - b\ Hence, we have RULE 3. The product of the sum and difference of two numbers is the différence of their squares. If we put 2x for a and 3 for b, we have Rule 1, (2x + 3)' = 43s + 12*...
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A School Algebra

George Albert Wentworth - Algebra - 1895 - 376 pages
...Differencc of Two Numbers. (a + ¿)(o- ¿) = a (a - ¿) + ¿(a - ¿) = a2 - ab + ab - ¿2 = a2-¿>2. Hence, we have RULE 3. The product of the sum and...numbers is the difference of their squares. If we put 2a; for o and 3 for b, we have Rule1, (2* + 3)2 = 4*4-12* + 9. Rule 2, (2* -3)2 = 4** -12* + 9. Rule3,...
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A School Algebra

George Albert Wentworth - Algebra - 1897 - 382 pages
...Sum and Difference of Two Numbers. (a + 6)(a— 6) = a (a -b) + b(ab) = a2 - ab + ab - 62 = a3 - tf. Hence, we have RULE 3. The product of the sum and...squares. If we put 2x for a and 3 for b, we have Rule 1, (2a; + 3)2 = 4^ + 12a; + 9. Rule 2, (2a;- 3)2 = 4a? -12a; + 9. Rule3, Exercise 19. Write the product...
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A Higher Algebra

George Albert Wentworth - Algebra - 1897 - 540 pages
...Numbers. (a + b)(a — ¿) = a (a - o) + S (a - 5) = a1 — ab + ab — V = a' - Ъ\ Hence we have KULE 3. The product of the sum and difference of two numbers is the difference of their squares. 82. Illustrations. If we put 2a; for a and 3 for b, we have Rule 1, (2x + 3y = 4z'+12x + 9. Rule 2,...
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