...in the square. By this notation we are enabled to express two distinct theorems by one formula. 69. The product of the sum and difference of two numbers is equal to the difference of their squares. Thus, if we multiply a+b by a — b a 2 +ab -ab-b 2 we obtain the product a 2 — b 2 . EXAMPLES. 2....

...by twice their product. Also we have (а+Ъ)(а-Ъ) = а"-Ъ'. Thus the product of the sum and the difference of two numbers is equal to the difference of their squares. 54. We may here indicate the meaning of the sign ± -which is sometimes used, and which is called the...

...the two numbers diminished by twice tJieir product. The last example gives Thus the product of tlw sum and difference of two numbers is equal to the difference of their squares. 80. The results of the preceding Article furnish a simple example of one of the uses of Algebra; we...

...in the square. By this notation we are enabled to express two distinct theorems by one formula. 69. The product of the sum and difference of two numbers is equal to the difference of their squares. Thus, if we multiply a+b by a—b a?+ab -ab-bz we obtain the product a2 — b2. EXAMPLES. 1. (3a+26)...

...being admitted ? Ans. ANN is HENBY'S wife, and MARY is R1CHARD'S. HANNAH is ROBERT'S. Premising that " the product of the sum and difference of two numbers is equal to the difference of their squares," and from the question we learn that the square of the yards bought by each wife is 63 less than the...

...9999997 by a complement. 19. Multiply 537486 by 1000800 by an excess. Art. 51. To square a given number. The product of the sum and difference of two numbers is equal to the difference of their squares. ALGEBRAIC DEMONSTUATION. NUMERICAL ILLUSTRATION. a + n 6 + 3=9 REMARK. « — n 6 — 3=3 Itisa principal...

...BD=mn. But (m + n) (mn)=m2-n? by multiplication, Henco the corresponding proposition in arithmetic is, The product of the sum and difference of two numbers is equal to the difference of their squares. 1. Let AC. CD be considered as two independent lines, then AD is their sum and DB is their difference...

...2 + x and 2—x? What are the factors of 4—x * ? 42. We see, from these examples, that theproduct of the sum and difference of two numbers is equal to the difference of their squares* Thus (xty)(x—y)— x'-y'. 5. Besolve 4z * —9y * into its factors. 6. Eesolve a*x* — c * y * into...

...product of 2 + x and 2—x? What are the factors of 4— a;8 ? 42. We see, from these examples, that the product of the sum and difference of two numbers is equal to th# difference of their squares. Thus (x+y)(xy)= xz-yz. 5. Resolve 4a;8— Qys into its factors. 6....

...point was the tree broken ? NOTE. — Solve this problem by the principle that the product of the suui and difference of two numbers is equal to the difference of their sauares. 71. Three men, A, B, and C, bought a grindstone three feet in diameter, paying equally; and...