...sum of the squares of the two number* diminished by twice their product. The last example gives Thus the product of the 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...

...product of 2 + x and 2—a;? What are the factors of 4—z* ? 42. We see, from these examples, that the product of the sum and difference of two numbers is equal to the difference of their squares* Thus (x+yXx—y)— x 8 -y'. 5. Resolve 4z * —9y * into its factors. 6. Resolve a *x s— c *y3 into...

...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 second have this connection...

...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 second have this connection...

...product of 2 + x and 2— x ? What are the factors of 4 — x2? 25. We see, from these examples, that the product of the sum and difference of two numbers is equal to the difference of their squares. Thus (x + y) X (x — y)—&1—-y2Ex. 1. What are the factors of 2a— 2b? 2. What are the factors...

...2+x and 2— x? What are the factors of 4—z 8 ? 42. We see, from these examples, thatthepnductofthe sum and difference of two numbers is equal to the difference of their squares. Thus (x+y)(xy)= x'-y2. 5. Kesolve 4a; s — 9y* into its factors. 6. Resolve a*x*—c 2 y a into its...

...яo — o(a + ¿>) = — ab — V Adding, (a + b) (a — b) — a' — V. (3) That is: THEOREM. Tlt-e product of the sum and difference of two numbers is equal to the difference of their squares. REMARK. The three preceding forms should be carefully memorized by the student, owing to their constant...

...their squares — twice their product. From (3) we have (a + ¿)(a — ¿) = o? — b2. That is, x 76. The product of the sum, and difference of two...numbers is equal to the difference of their squares. 78. By using the double sign rb, read plus or minus, we may represent (1) and (2) by a single formula...

...equat, to the sum of their squares — twice their product. From (3) we have (a + ¿)(a — ¿) = a2 — b*. That is, 76. The product of the sum and difference...numbers is equal to the difference of their squares. 78. By using the double sign rfc, read plus or minus, we may represent (1) and (2) by a single formula...

...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 Hie difference of their squares. Thus, if we multiply a + b by a — b -ab-bz are obtain the product...