...power or square of the sum of two quantities contains the square of the first quantity, plus double the product of the first by the second, plus the square of the second. Thus, (7 + 3) (7 + 3) or, (7 + 3)' = 49 + 42 + 9 = 100 So also (5 a2 + 8 a2 6)2 = 25 a6 + 80 <tb +...

...enunciated in another manner : viz. The square of any polynomial contains the square of the first term, plus twice the product of the first by the second, plus the square of the second; plus twice the product of each of the two first terms by the third, plus the square of the third; plus...

...principles, (a+by=(a+b) (a+b)=a3+'2ab+b3. That is, the square of the sum of two quantities is composed of the square of the first, plus twice the product of...first by the second, plus the square of the second. Thus, to form the square of 5a3+8a3i, we have, from what has just been said, 2d. To form the square...

...required 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...first by the second, plus the square of the second. Thus, to form the square of 5a"-\-8a2b, we have, from what has just been said, 2d. To form the square...

...required 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...first by the second, plus the square of the second. 1. Form the square of 2a+36. We have from the rule (2a + 36)2 = 4<z3 + 12ab + 962. 2. (5a6 + 3<zc)2...

...is, the square of the difference between two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second. Thus, (7o3i3— 12ai3)3=49o4i4— 168a3i5+144a3i6. 3d. Let it be required to multiply a-\-b by a —...

...required 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...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...

...power of 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...first by the second, plus the square of the second. Thus, to form the square of 5o 2 +8a 2 i, we have, from what has just been said, (5a 2 + 8a 2 i) 2...

...required 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...first by the second, plus the square of the second. 1. Form the square of 2a+36. We have from the rule (2a + 36)2 = 4a2 + 12a6 + 962. 3. (5a6+3ac)2 =25a262+...

...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...first by the second, plus the square of the second. 17. Multiply a — b by a — b. The product is a2 — 2a6+62 ; from which we perceive, that the square...