'^12 AlGEBllA. 



•z. Let >:• — .7 be involved to the slxtli powei** 



The terms without the coefficients will be 

 a;^, X^ch X^^a^ x'a'f fic^i"^, xa^y a^ ^ 

 and the coellicients Vv-i]l be 

 . 6X5 1^X4 20x3 15x2 6XJ 



2 3 4 5 6 



or I, 6, 15, 20, 15, 6, I ; 

 And therefore the 6th power of a,' — -a is 



3. Find the 4th power of x — a. 



Alls. X * -^4.^ "^ ^ •4-6rv "" a ^ *-^4J^^ ^ -^-a ^ . 



4. Find the 7th power of Ar+/7. 



Ans. A'^-j-7.v^^^+ 2 lAJ^rt ^4-3 s-v'^.z ^ -f-3 5^' ' '^''^+ 2 ^ -v * ^r 



EVOLUTION. 



Evolution is the reverse of involution, and teaches to 

 find the roots of any given powers. 



CASE I. 

 To find the rovts of simple quantities, 



RULE.* 



Extract the root of the coefficient for the numerical 

 part, and divide the indices of the letters by the index of 

 the power, and it will give the root required. 



EXAMPLES. 



* Any even root of an affirraative quantity may be either -f- <»* 

 — : thus, the square root of 4-^* is either 4-^, or —a; for 



And 



