 | Joseph Ray - Algebra - 1848 - 252 pages
...THEOREM II. The square of the difference of two quantities, is equal to {he square of the first, minus twice the product of the first by the second, plus the square of the second. EXAMPLES. 1. (5-4)2=25-40+16=l. 2. (2a— 6)2=4a2 3. (3x-2y)2 4. (al-yI)»=z 5. (ax— x*Y=aW— 2axs+a;«.... | |
 | Algebra - 1848 - 394 pages
...rules for the multiplication of algebraic quantities in the demonstration of the following theorems. THEOREM I. The square of the sum of two quantities is equal to the squarg vf the first, plus twice the product of the first by the second, plut the square of the second.... | |
 | Rufus Putnam - Arithmetic - 1849 - 402 pages
...+ 3)*. From these examples and illustrations, wo see that the square of the sum of any two numbers is equal to the square of the first, plus twice the product of the first into the second, plus the square of the second. 5. Find by this method the square of4-f-3; 5-f-8; lf-4;... | |
 | Stephen Chase - Algebra - 1849 - 348 pages
...have (a+6) 2 = (a+J) (a+J) = a2+2ab+b2. That is, THEOREM I. The square of the sum of two numbers i> equal to the square of the first, plus twice the product of tlte Jirst by the second, plus the square of the second. Or, more briefly, The square of the sum of... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...the product will be o2+2a6+62 ; thus : a+b But a-\-b is the sum of the quantities, a and b : hence THEOREM I. The square of the sum of two quantities,...twice the product of the first by the second, plus thz square of the second. EXAMPLES. NOTE. — The instructor should read each of the following examples... | |
 | New York (State) School for the deaf, White Plains - 1854 - 936 pages
...gives minus." (b-— 1)=! (If— 1)=(&6— &s)." What is the square of the sum of two quantities T " The square of the sum of two quantities is equal to...first by the second, plus the square of the second." (la— 5Z>)S= what! " (la— 5Z>)3= 49as— 70ab+25b\" Resolve a2 — b~ into factors 1 What is the... | |
 | Jeremiah Day - Algebra - 1854 - 428 pages
...relate to certain cases in Multiplication of frequent occurrence, and should be carefully learned. THEOREM I. The square of the Sum of two quantities...square of the first, plus twice the product of the jirst and second, plus the square of the second. This may be expressed algebraically thus, (a+b)3=a3+2ab+b3,... | |
 | James William M'Gauley - 1854 - 284 pages
...algebraic formula [sec. 1, 1], — For, the result of the multiplication may be read as follows : — " the square of the sum of two quantities is equal to the sum of their squares, plus twice their product." And as the given quantities may represent any possible... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...following Theorems are of such extensive application that they should be carefully committed to memory. THEOREM I. The square of the sum of two quantities...first by the second, plus the square of the second. Thus, if we multiply a + b By a + b a'+ ab _ We obtain the product a'+lab+b". Hence, if we wish to... | |
 | Dana Pond Colburn - Arithmetic - 1855 - 396 pages
...the second, and b2 equals the square of the second ; The square of the sum of any two numbers equals the square of the first, plus twice the product of the first by the second, plus the square of the tecond. Illustrations. (7 + 5)2 = 72 + 2 X 7 X 5 + 52 = 49 + 70 + 25 = 144 = 122 (8 -f- 4)a = 82 +... | |
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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. 
