Question

Упростить выражение (x^2+5*x+2)^2+(x^2-5*x-2)^2-2*(5*x+2)^2

Answer 1

(х²)²+2×х²×(5х+2)+(5х+2)²+(х²)²-2×х²×(5х-2)+(5х-2)²-2×((5х)²+2×5х×2+(2)²)=х⁴+10х³+4х²+(5х)²+2×5х×2+2²+х⁴-10х³+4х²+(5х)²-2×5х×2+2²-2×(25х²+20х+4)=х⁴+10х³+4х²+25х²+20х+4+х⁴-10х³+4х²+25х²-20х+4-2×(25х²+20х+4)=2х⁴+58х²+8-50х²-40х-8=2х⁴+8х²-40х=2х×(х³+4х-20)