...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,...

...to form the square or second power of the binomial, (a+*)- 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 first by the second, plus the square of the second. Thus, to form the square of 5a"-\-8a2b, we have,...

...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...

...to form the square or second power of the binomiaj (a+b). 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 first by the second, plus the square of the second. 1. Form the square of 2a+36. We have from the rule...

...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,...

...the binomial, (a-\-b). We have, from known principles, (a + b)2=(a+b) (a+i)=a 2 +2ai+i 2 . That is, the square of the sum of two quantities is equal to...square of the first, plus twice the product of the first by the second, plus the square of the second. Thus, to form the square of 5o 2 +8a 2 i, we have,...

...to form the square or second power of the binomial (a-\-b). 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 first by the second, plus the square of the second. 1. Form the square of 2a+36. We have from the rule...

...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...square of the first, plus twice the product of the first by the second, plus the square of the second. Let a denote one of the quantities and l1 the other:...

...14a26c5+14a62c5— 3a2ce— 7 16. Multiply a+6 by a+b. The product is a2+2a6-}-62; from which it appears, that the square of the sum of two quantities, is equal...square of the first plus twice the product of the first by the second, plus the square of the second. 17. Multiply a — b by a — b. The product is...