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Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
A Treatise on Algebra - Page 139
by Elias Loomis - 1873 - 360 pages

Elements of Algebra

Bourdon (M., Louis Pierre Marie) - Algebra - 1839 - 368 pages
...proves that the square of a number composed of tens and units contains, the square of the tens phis twice the product of the tens by the units, plus the square of the units. 117. If now, we make the units 1, 2, 3, 4, &c., tens, by annexing to each figure a cipher, we shall...

An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - Algebra - 1841 - 320 pages
...625. When, therefore, a number contains tens and units, its sccnnd power will contain the second power of the tens, plus twice, the product of the tens by the units, plus the second power of the units. Now let us reverse the process, and see by what means the root could be...

Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1842 - 284 pages
...(a+6)2=(64)2; or a2 + Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units. 94. If, now, we make the units 1,2, 3, 4, &c, tens, or units of the second order, by annexing to each...

Elements of Algebra

Charles Davies - Algebra - 1842 - 368 pages
...and (a+i) 3 =(64) 3 , Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of ihe units. 117. If now, we make the units 1, 2, 3, 4, &c., tens, by annexing to each figure a cipher,...

Charles Davies - Arithmetic - 1844 - 666 pages
...square AE, the two rectangles FE and EC, and the square ED : Hence The square of two figures is equal to the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. Let it now be required to extract the square i^oi of 1296. Since the number contains more than two...

Elements of Arithmetic: For Schools and Academies. In which Decimal and ...

Pliny Earle Chase - Arithmetic - 1844 - 246 pages
...the 7 in the root, and also at the right of the divisor, we multiply by 7, and obtain 469, which is twice the product of the tens by the units plus the square of the units. Hence we deduce the following RULE. Separate the number into periods of two figures each, by placing...

Elements of Algebra: Embracing ... the Theory and Application of Logarithms ...

Davis Wasgatt Clark - 1844 - 394 pages
...Subtracting the square of this - - - 2116 Square of 4 tens, or 40 - - - - 1600 516 This remainder contains twice the product of the tens by the units, plus the square of the units. Now, if we double the tens, which gives 80, and divide 516 by 80, the quotient is the figure of the...

Smith and Duke's The American Statistical Arithmetic: Designed for Academies ...

Francis Henney Smith - Arithmetic - 1845 - 300 pages
...for any other number, we conclude, that the square of a number composed of tens and units contains the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. Q. Of what parts may every number be considered as composed ? What does 16 contain 1 251 59? 125 ?...