...Zab + V. . . . (B), which expresses the Rule :—Tlie square of the difference of two quantities is the square of the first, minus twice the product of the first by the second, plus the square of the second. Ex. 1. (x - 5)" = x' - 10ж + 25. Ex. 2. (За - 2o)" =...

...За3Я Result, 5. Square %ab~* + f х- »ОЧ Result, 9o. Theorem. — The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first Ъу the second, plus the square of the second. Demonstration.— Let ж and у be any two quantities....

...4. (5a2+2J)2= 9. 5. (5a3+b)z=- 10. 67. The square of the difference of two numbers is equal to th& square of the first, minus twice the product of the first by the second, plus the square of the second. Thus, if we multiply a—b by a— 6 ~a?^-ab - ab+W •we...

...plus the square of the second. Likewise we learn that which means that the square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second. 128. Reversing these two formulas, we have A 2 + 2 AB +...

...the product of the two, plus the square of the second. 86. THEO. — The square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second, 87. THEO. — The product of the sum and difference of two quantities...

...i4 4- 6 a5 #" c4 -f-- 9 a4 4*c". THEOREM II. 77i The square of the difference of two quantities il equal to the square of the first, minus twice the product of the first by the second, plus the square of the second. For, let a represent one of the quantities, and b the other;...

...the second case, we have (a — 6)2 = a2 — 2 ab + 62. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second. In the third case, we have (a -\-b)(a — b) = a2 — 62. (3) That...

...the second case, we have (a — 6)2 = a2-— 2 ab + b2. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That...

...the second case, we have (a — 6)2 = a2 — 2 ab + b3. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That...

...+ 4 = 5184. (104)2 = (100 + 4)2 = 10000 + 800 + 16 = 10816. 88. II. The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second. Thus, (x — yY = a* — 2xy + y2. g. (x — 5) (x- 3) =...