...somewhat more complicated formula, such as (a + b)2=a? + 2ab + b2, which would be thus stated in words : " The square of the sum of two numbers is equal to the sum of their squares increased by twice the product of the numbers", the advantage is more decidedly...

...the first and second have this connection : (а+Ьу = (а-Ь)>+4аЬ, (e-î)l = (e+J)1-4ei; that is, The square of the sum of two numbers, is equal to the sum of tho square of the difference and four times the product of the two numbers. Tho square of the...

...And the first and second have this connection : (a+J)2 = (e_i)»+4ei, (ei)' = (e+i)I-4ei; that ie, The square of the sum of two numbers, is equal to the sum of the square of the difference and four times the product of the two numbers. The square of the...

...b' The first example gives the value of (a + £>) (a + 6), that is, of (a + b)' ; we thus find Thus the square of the sum of two numbers is equal to the sum of the squares of the two numbers increased by twice t/ieir product. Again we have Thus the square...

...as many decimal figures are obtained as the degree of accuracy necessary in the result may require. The principle on which the preceding rule depends,...the square of the sum of two numbers is equal to the sum of the squares of the numbers added to twice their product. Thus, 34 being = 30 + 4, its square...

...602+60X4 4096= = 3600 + 480+16. The operations illustrate the following principle : PRINCIPLE. — The square of the sum of two numbers is equal to the square of Hie first, plus twice the product of the first by the second, plus tiie square of the second....

...three which follow are of great importance: From (1) we have (a + bf = a? + 2ab + b2. That is, 74. The square of the sum of two numbers is equal to the sum of their squares + twice their product. From (2) we have (a — 6)2 = a' — 2 ab + 62. That is,...

...added units. We shall soon require the following important theorem relating to the squares of numbers. The square of the sum of two numbers is equal to the sum of the squares of the number together with twice the product of the numbers. For instance 1 1 is...

...follow are of great importance : Ь' à2 - Ь2 From (1) we have (a + ¿)2 = a2 + 2ab + V. That is, 74. The square of the sum of two numbers is equal to the sum of their squares + twice their product. From (2) we have (a - ¿)2 = a2 — 2 ab + b\ That is,...

...a + 6 we get (« + 6) (a + 6) = «2 + 2a6 + 62 ; that is (a + 6)2 = a2 + 2«6 + 62. . . . (1) Thus the square of the sum of two numbers is equal to the sum of the squares of the two numbers increased by twice their product. Similarly, if we multiply a...