 ... 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 is, the product of the sum and difference of two quantities is equal to the difference of their squares.  A Treatise on Algebra - Pàgina 189per Elias Loomis - 1846 - 346 pàginesVisualització completa - Sobre aquest llibre
 | James Bates Thomson - 1878 - 322 pàgines
...Multiply loth terms of the fraction by such a factor an will make the required term rational. NOTE — Since the product of the sum and difference of two...quantities is equal to the difference of their squares, when the radical fraction is of the form — = -- -, if we multiply the terms by -y/ 'a — V& (\/a... | |
 | Edward Olney - 1878 - 360 pàgines
...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 is equal to the difference of their squares. EXAMPLES. 1. Multiply together Ъах, — 3a*xs, kby, — y3, and 2z*y9. • 2, Multiply together... | |
 | Benjamin Greenleaf - 1878 - 338 pàgines
...the square of 5 a2 i2 — 10 a2 V ? Ans. 25 a4 64 — 100 a4 b% + 100 a4 66. THEOREM III. 78i TJ1e product of the sum and difference of two quantities is equal to the difference of their squares. For, let a represent one of the quantities, and 6 the other ; then, (a + 6) X (« — 6) = «' —... | |
 | Edward Olney - 1878 - 516 pàgines
...— b EXPLANATION. — I observe that a — vft will be rationalized by multiplying it by a + */b, since the product of the sum and difference of two quantities is the difference of their squares. Hence multiplying both terms of the fraction, so as not to alter its... | |
 | Thomas K. Brown - 1879 - 292 pàgines
...difference of the squares of the two quantities. This may be more briefly expressed thus : Theorem III. — The product of the sum and difference of two quantities is equal to the difference of their squares. SECTION XXVIII. USE OF THEOREMS IN MULTIPLICATION. 77. Ex. What is the square of x + y ? SOLUTION,... | |
 | Webster Wells - 1879 - 468 pàgines
...first by the second, plus the square of the second. 106. Again, by multiplication, we have That is, The product of the sum and difference of two quantities is equal to the difference of their squares. EXAMPLES. 107. 1. Square 3 a + 2 b. The square of the first term is 9 a2, twice the product of the... | |
 | Wisconsin - 1879 - 1240 pàgines
...sides are together equivalent to the squares of the diagonals. 2. Demonstrate, geometrically, that the product of the sum and difference of two quantities is equal to the difference of their squares, 3. Prove that, if from the same point without a circle a tangent and a secant be drawn, the tangent... | |
 | Wisconsin. Department of Public Instruction - 1879 - 380 pàgines
...sides are together equivalent to the squares of the diagonals. 2. Demonstrate, geometrically, that the product of the sum and difference of two quantities is equal to the difference of their squares. 3. Prove that, if from the same point without a circle a tangent and a secant be drawn, the tangent... | |
 | Benjamin Greenleaf - 1879 - 350 pàgines
...containing only the square root. 1. Rationalize \/a -f- \/b. OPERATION. Since the product of the earn and — , difference of two quantities is equal • '- to the difference of their squares y/g — y/6 (Theo. III. Art. 78), we multiply the i j—l given binomial by the same terms. with one... | |
 | Benjamin Greenleaf - 1879 - 350 pàgines
...root. 1. Rationalize \/a -\- \/b. Explain the first operation. The second. Repeat the Rule. OPERATION. Since the product of the sum and — difference of two quantities is equal Va + V* to the difference of their squares у*а — y'6 (Theo. III. Art. 78), we multiply the i ,... | |
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