 | Edward Olney - 1878 - 360 σελίδες
...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 σελίδες
...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 σελίδες
...sum and difference of their square roots. DEM. — This is an immediate consequence of the theorem, that "The product of the sum and difference of two quantities is the difference of their squares." Thus a2 — lP = (a-\-b}(a — 6). Also, if we have m — n, m is... | |
 | Wisconsin - 1879 - 1240 σελίδες
...of the 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 σελίδες
...of the 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... | |
 | Webster Wells - 1879 - 468 σελίδες
...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... | |
 | Thomas K. Brown - 1879 - 292 σελίδες
...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,... | |
 | Benjamin Greenleaf - 1879 - 350 σελίδες
...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 σελίδες
...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 ,... | |
 | Shelton Palmer Sanford - 1879 - 348 σελίδες
...Ans. - . 20. Square (a" - 1). Ans. a»n - 2a" + 1. THEOREM III. 69. The product of the SUM and the DIFFERENCE of two quantities is equal to the difference of their squares. Ex. 1. What is the product of (a +6) multiplied by (a- 6)? OPERATION. a + 6 Analysis. Multiplying (a... | |
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... 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. 
