разложите ** множители: 81(2k+1)2-(k-3)2 (8p-5)2-9(3p+2)2

Question

разложите на множители:

81(2k+1)2-(k-3)2

(8p-5)2-9(3p+2)2

Answer 1

81(2k+1)2-(k-3)2

81(2k+1)^2-(k-3)^2=(9(2k+1)-k+3)(9(2k+1)+k-3)=
=(18k+9-k+3)(18k+9+k-3)=(17k+12)(19k+6).

 

(8p-5)2-9(3p+2)2

((8p-5)-3(3p+2))(8p-5)+3(3p+2))=
=(8p-5-9p-6)(8p-5+9p+6)=-(p+11)(17p+1) .