Elements of Algebra

CHAP. VII. \quad OF ALGEBRA. \quad 101 to the first term $2a$; but as soon as the quotient is found, which in the present case is $b$, we must put it in the vacant place, and thus render the division complete. 321. The calculation, therefore, by which we find the root of the square $a^2 + 2ab + b^2$, may be represented thus: $a^2+2ab+b^2(a+b$ $a^2$ --- $2a+b)$ $2ab+b^2$ $2ab+b^2$ --- $0.$ 322. We may, also, in the same manner, find the square root of other compound quantities, provided they are squares, as will appear from the following examples: $a^2+6ab+9b^2(a+3b$ $a^2$ --- $2a+3b)$ $6ab+9b^2$ $6ab+9b^2$ --- $0.$ $4a^2-4ab+b^2(2a-b$ $4a^2$ --- $4a-b)$ $-4ab+b^2$ $-4ab+b^2$ --- $0.$ $9p^2+24pq+16q^2(3p+4q$ $9p^2$ --- $6p+4q)$ $24pq+16q^2$ $24pq+16q^2$ --- $0.$ $25x^2-60x+36(5x-6$ $25x^2$ --- $10x-6)$ $-60x+36$ $-60x+36$ --- $0.$