...power or square of the sum of two quantities contains the square of the first quantity, plus double the product of the first by the second, plus the square of the second. Thus, (7 + 3) (7 + 3) or, (7 + 3)' = 49 + 42 + 9 = 100 So also (5 a2 + 8 a2 6)2 = 25 a6 + 80 <tb +...

...(a+b)=a3+'2ab+b3. That is, the square of the sum of two quantities is composed of the square of the first, plus twice the product of the first by the second, plus the square of the second. Thus, to form the square of 5a3+8a3i, we have, from what has just been said, 2d. To form the square...

...(a+b)=a? + 2ab+b\ That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second. 1. Form the square of 2a+36. We have from the rule (2a + 36)2 — 4a2 + 12ab + 962. 2. (5a6+3ac)2 =...

...third forms, we see that the first member in each contains two terms of the square of a binomial, viz : the square of the first term plus twice the product of the 2nd term by the first. If, then, we take half the coefficient of x, viz : p, and square it, and add...

...by x + a, we shall have (x + a)3 = x3 + 2 ax + a' ; that is, the square of a binomial, is made up of the square of the first term, plus twice the product of the two terms, plus the square of the last term. This suggests the rule for extracting the square root...

...; being true for four, it is necessarily true for^ce, and so on. Therefore it is general. This law can be enunciated in another manner : viz. The square...square of the first term, plus twice the product of thefirst by the second, plus the square of the second ; plus twice the product of thefirst two terms...

...third forms, we see that the first member in each contains two terms of the square of a binomial, viz : the square of the first term plus twice the product of the 2nd term by the first. If, then, we take half the coefficient of x, viz : p, and square it, and add...

...(a+4+c+</)'=a2+2aA+42+2(a+4)c+c2+2(a+4+c)a"+d!, The square of a polynomial expression is consequently composed of the square of the first term, plus twice the product of the first term by the second, plus the square of the second term, plus twice the product of the sum of the first...

...represent any numbers whatever, we infer the following general principle : The square of a binomial is the square of the first term, plus twice the product of the two terms, plus the square of the last tern 4. Required the second power of a— b. a — b a—b 2—...

...which it appears, that the square of the sum of two quantities, is equal to the square of the first plus twice the product of the first by the second, plus the square of the second. 17. Multiply a — b by a — b. The product is a2 — 2a6+62 ; from which we perceive, that the square...