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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.
Elements of Algebra - Page 112
1838 - 355 pages

## Elements of Algebra

Silvestre François Lacroix - Algebra - 1818 - 422 pages
...tens plus the unite, or 2 a + b ; this multiplied by 7 or 6, reproduces 609 = 2 ab + 62, or double the product of the tens by the units, plus the square of the units. This being subtracted leaves no remainder, and the operation shows, that 47 is the square root of 2209....

## Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...the tens plus the units, or 2 a + b ; this multiplied by 7 or b, reproduces 609 = 2a6 + 6s, or double the product of the tens by the units, plus the square of the units. This being subtracted leaves no remainder, and the operation •hows, that 47 is the square root of...

## A Theoretical and Practical Arithmetic: In which the Principles of that ...

Bézout - Arithmetic - 1825 - 258 pages
...add these products, and we have, for the square, the number 2916, which, as we see, is composed of the square of the tens, plus twice the product of...the tens by the units, plus the square of the units of the number 54. 134. What we have, observed being an immediate consequence of the rules of multiplication,...

## Elements of Algebra

William Smyth - Algebra - 1830 - 278 pages
...62=2209. Thus the square of a number, consisting of units and tens, is composed of three parts, viz. the square of the tens, plus twice the product of the tens multiplied by the units, plus the square of the units. Thus in 2209, the square of 47, we have The...

## The Youth's Assistant in Theorhetic [sic] and Practical Arithmetic: Designed ...

Zadock Thompson - Arithmetic - 1832 - 186 pages
...appears that the square of a number consisting of tens and units is made up of the square of the units, plus twice the product of the tens, by the units, plus the square of the tens. See this exhibited in figure F. As 10X 10=100, the square of the tens cau never make a part of...

## The Youth's Assistant in Theoretic and Practical Arithmetic: Designed for ...

Zadock Thompson - Arithmetic - 1832 - 186 pages
...appears that the square of a number consisting of tens and units is made up of the square of the units, plus twice the product of the tens, by the units, plus the square of the tens. See this exhibited in figure F. As 10X 10=100, the square of the tens can never make a part of...

## A New Introduction to the Science of Algebra ...

Silas Totten - Algebra - 1836 - 320 pages
...the units, we shall have, for the square of a + b, a3 + 2ab + b ; that is, the square of the tens, twice the product of the tens by the units, plus the square of the units. Let a = 8, and 6 = 5: then, since a represents the tens, and b the units, a + b becomes 80 + 5 = 85...

## First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 272 pages
...1 What arc rhey 1 Now, if we represent the tens by a and the units by b, we shall have a+b =64, and Which proves that the square of a number composed...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...

## First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 264 pages
...w/ represent the tens by a and the units by b, we shall have a+b =64, and (a+6)2=(64)2; or a*-fWhich proves that the square of a number composed of tens...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...

## 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...