...Square of the other Part, is equal to the Squares of the Sum of the whole and that Part. THEOREM V. THE Square of the Sum of two Numbers is equal to the Sum of the Square of one of them • and the Product of thé other into the Sum of this other and double...

...of two quantities is composed of the square of the first added to the square of the second, added to twice the product of the first by the second. The square of 5 a3 -f- 8 a2 b will be found to be, 25 a6 + 80 a5 6 +64 a4 62. (2.) The square of « — b. (a —...

...Answer. 1 1 1 23 71 69 2608 | 20864 20864 * The principle on which the preceding rule depends is, that the square of the sum of two numbers is equal to the squares of the numbers with twice their product. Thus, the square of 34 is equal to the squares of...

...its circumference to be 24880 miles ? Ans. 7919.53666 miles, nearly. Extraction of the Square Root. The square of the sum of two numbers is equal to the squares of the numbers with twice their product. Thus, the square of 24 is equal to the squares of...

...be seen that the square of a polynomial of three terms is composed of the square of the first term, twice the product of the first by the second, the square of the second, twice the product of the first by the third, twice the product of the second by the third, and the...

...From these examples we see that the product of the sum of two numbers, by their sum, that is to say, the square of the sum of two numbers, is equal to the sum of their squares added to twice their product. 0+6 12 + 8 a —b 12 — 8 114 — 96 — 96 —...

...accuracy necessary in the result muy require. Tke pnnniJe on which the preceding rule depends, is, that the square of the sum of two numbers is equal to the squares of the numbers with twice their product. Thus, the square of 34 is equal to ttie squares of...

...their sum, by their sum. a+b a+b a3+ab +ab+b3 By this operation we find the following general property. The square of the sum of two numbers is equal to the square of the Jlrst number, plus twice the product of the two numbers, plus the square of the last number. §173....

...into a + b, or the square Square of (Art. 39.) of a + b. a + 6' a + b a + b a* + ab + ab + b* = (a Or the square of the sum of two numbers is equal to the sum of the squares of those numbers together with twice their product. Thus, (5 + S)8 = 25 + 9 + 2x3x5=...

...) , . ,, ,, , n ^ a +0=0 -\-2p. gether ) Fifth Theorem. 201. The square of a polynomial expressing the sum of two numbers, is equal to the square of the fIrst term -f twice the product of the two terms + the square of th2 last term. Let s represent the sum,...