Question

Разложите на множители
a) 18а^2+24а+8-200b^2
b) 126x^3+3x^2+3x+1

Answer 1

$18a^2+24a+8-200b^2=2(9a^2+12a+4-100b^2)=2((3a+2)^2-100b^2)= \ =2(3a+2-10b)(3a+2+10b) \\ 126x^3+3x^2+3x+1=125x^3+x^3+3x^2+3x+1=125x^3+(x+1)^3= \ =(5x+x+1)(25x^2-5x(x+1)+(x+1)^2)= \ =(6x+1)(25x^2-5x^2-5x+x^2+2x+1)=(6x+1)(21x^2-3x+1)$