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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

## Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1848 - 300 pages
...which we bring down the two next figures 84. The result of this operation, 1184, contains twice t/te product of the tens by the units^ plus the square of the units. * But since tens multiplied by units cannot give a product of a less name than tens, it follows that the...

## Arithmetic: Designed for Academies and Schools, Uniting the Inductive ...

Charles Davies - Arithmetic - 1848 - 372 pages
...rectangles FE and EC, and the square ED. Hence, 30 The square of two figures is equal to the square of ths tens, plus twice the product of the tens by the units, plus tht square of the units. Let it now be required to extract the square root of 1296. Since the number...

## The University Arithmetic: Embracing the Science of Numbers, and Their ...

Charles Davies - Arithmetic - 1850 - 412 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 root of 1296. Since the number contains more than two...

## Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1850 - 292 pages
...1 , 0~ to which we bring down the two next figures 84. The result of this operation, 1184, contains twice the product of the tens by the units, plus the square of the units. But since tens multiplied by units cannot give a product, of a less name than tens, it follows that the...

## School Arithmetic: Analytical and Practical

Charles Davies - 1852 - 344 pages
...sum is 32+2(3 x 6)+62 : that is, 3 + 6 3 + 6 32+3x6 3'+2(3x6)+6 H The square of a number is equal to the square of the tens, plus twice the product of...the tens by the units, plus the square of the units. The same may be shown by the figure : Let the line AB re- F 30 IP present the 3 tens or 30, and BC...

## The Decimal System of Numbers: Illustrated and Practically Applied, by a ...

Dana Pond Colburn - Arithmetic - 1852 - 228 pages
...the same units' figure, must equal the product of the tens by the tens, plus the product of the sum of the tens by the units, plus the square of the units. Show the truth of the following equations : — 67 times 37 = 60 times 30 -f- 7 times 90 + 7 times...

## The Theoretical and Practical Systematic Arithmetic; Or, Arithmetic Arranged ...

David Henry Cruttenden - Arithmetic - 1853 - 330 pages
...square of 45. Thus, 45 = 40+ 5 40+ 5 200 + 25 1600 + 200 Hence, 452 = 1600+400 +25=2025 Ans. That is, the square of the tens, plus twice the product of the tens into the units, plus the square of the units. 16. What is the 4th power of 12 ? Ans. 20,736. 17. Find...

## Common School Algebra

Thomas Sherwin - Algebra - 1855 - 262 pages
...+ 9 = 529. Hence, When a number contains units and tens, its second power contains the second power of the tens, plus twice the product of the tens by the units, plus the second power of the units. Let us now, by a reverse operation, deduce the root from the power. Operation....