 ... 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.  Elements of Algebra - Page 100by William Smyth - 1847Full view - About this book
 | William Frothingham Bradbury - 1875 - 280 pages
...-|- y2. 2. 2 ж — 4 у. 3. ж— 1. Ans. x2 — 2ж + 1. 4. 7ж-2. <# THEOREM IV. ^ ¿A 60i ÎTie product of the sum and difference of two quantities is equal to the difference of their squares. Let a -|- 6 be the sum, and a — 6 the difference of the two quantities a and h. PROOF. a... | |
 | Edward Olney - Algebra - 1877 - 466 pages
...— 12а"Ь~" + 96~7. 4. Square m ~p — n~q. Result, т-" — 2т~гп-' + п~*. lm 96. THEO. — The product of the sum and difference of two quantities is equal to the difference of their squares. DEM. — Let x and y be any two quantities. Their sum is x -\- y, and their difference is... | |
 | William Frothingham Bradbury - Algebra - 1877 - 280 pages
...y1. 2. 2 x — 4 у. 3. a;— 1. Ans. x2 — 2x + 1. 4. 7x — 2. THEOREM IV. 60. Tlw product of tlie sum and difference of two quantities is equal to the difference of their squares. Let a -j- b be the sum, and a — b the difference of the two quantities a and It. PROOF.... | |
 | James Bates Thomson - Algebra - 1878 - 322 pages
...Radical Binomial to a Rational Quantity. i. It is required to rationalize \/« + Vb. ANALYSIS. — The product of the sum and difference of two quantities is equal to the difference of their squares (Art. 103) ; therefore, (y'aH <\/&) multiplied by ( y^-y's) = a— 6, which is a rational quantity.... | |
 | Edward Olney - 1878 - 360 pages
...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... | |
 | Benjamin Greenleaf - 1878 - 338 pages
...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) =... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...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... | |
 | Wisconsin. Department of Public Instruction - Education - 1879 - 380 pages
...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... | |
 | Wisconsin - Wisconsin - 1879 - 1240 pages
...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... | |
 | Thomas K. Brown - Algebra - 1879 - 292 pages
...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,... | |
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