...other. This is the square of a + b (Art. 11), and the result may be expressed in words, as follows : " The square of the sum of two quantities is equal to the sum of the squares of the two quantities, together with twice their product.1"* (2) To find the square...

...4a6a) x (7asb + 4a62) = 49a«6s — 16а»ЬЧ The following properties are also of great use : — 1. The square of the sum of two quantities, is equal to the sum of their squares plus twice their product. Let a and b be the quantities, then a -fb is theipsum,...

...will be useful exercises. It is required to prove 1°. That (a + 6) (n + b) = os + lab + 63 ; or, that the square of the sum of two quantities is equal to the square of the first quantity, plus the square of the second, plus twice the product of the first and second. 2°. That...

...or second power of the binomial, (a-\-b). We have, from known principles, That is, the square ofthe sum of two quantities is equal to the square of the first, plus twice the product of tl>e first by the second, plus the square of the second. Thus, to form the square of 5a2+8a26, we have,...

...to form the square or second power of the binomial (a+6). We have, from known principles, That is, the square of the sum of two quantities is equal to...square of the first, plus twice the product of the frst by the second, plus the square of the second. 1. Form the square of 2a+3J. We have from the rule...

...quantities, is equal to the difference of the squares of those quantities." From the 2nd of these we see that "The square of the sum of two quantities, is equal to the sum of their squares, plus twice their product." From the 3rd of these we see that "The square of the...

...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...to the square of the first, plus twice the product j)f the first by the second, plus the square of the second. Thus if we multiply a + b By a + b a2 -\-...

...rules for the multiplication of algébrale quantities in the demonstration of the following theorems. THEOREM I. The square of the sum of two quantities is equal to the square of the ßrst, plus twice the product of the ßrst by the second, plus the square of the second. : Let a denote...

...to form the square or second power of the binomial (a+i). We have, from known principles, That is, the square of the sum of two quantities is equal to the square of the jlrst, plus twice the product of the first by the second, plus the square of the- second. 1. Form the...

...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....