Factorization x 5 to the fourth power x 3 to the fourth power 82.

x+5)^4+(x+3)^4-82

Use the commutation method to set a=x+3

then a+2) 4+a 4-81-1

a^2+4a+5）（a+3）（a+1）+（a^2+9）（a+3）（a-3）

a+3）〔 a^2+4a+5）（a+1）+（a^2+9）（a-3） 〕

a+3)(a 3-1+a 2-1+9a-9)(a+3)((a-1)(a 2+a+1)+a+1+9)(a+3)(a-1)(a 2+2a+11) Finally, x+3=a can be brought in.

x+5) to the fourth power + (x+3) of the fourth Zen Mountain radical formula + 82 Evergrande at 0, there is no solution but containment, so it cannot be factored to congratulate the socks solution. But (x+1) 4+(x+3) 4 - 82 =[x+1) 4-1 4]+[x+3) 4-3 4]=[x+1) 2+1 2][(x+1) 2-1 2]+[x+3) 2+3 2][(x+3) 2-3 2]=[x+1) 2+1 2](x+1+1)(x+1-1)+[x+..].

x 4+4x 3+4x 2 -9= x 2(x 2+4x+4) -9= x 2(x+2) 2 -9= [x(x+2)] 2 -9= (x 2+2x) 2 -9= (x 2+2x+3)(x 2+2x-3)= x 2+2x+3)(x+3)(x-1)--Sort out knowledge and help others, Delight yourself. The "Mathematics and Physics Infinite Exaggeration Front" team welcomes you to congratulate you.

x 4 is the meaning of x to the fourth power).

Original = x 4+x 2+x 2-x 2+1+1-x 3x 4+2x 2+1-x 2+1-x 3

x^2+1)^2-x^2+(1-x)(1+x+x^2)(x^2+1-x)(x^2+1+x)+（1-x)(1+x+x^2)(x^2+1-x+1-x)(x^2+x+1)(x^2-2x+2)(x^2+x+1)

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(x+5)^4+(x+3)^4-82

Use the commutation method. Let a=x+3

then a+2) 4+a 4-81-1

a^2+4a+5）（a+3）（a+1）+（a^2+9）（a+3）（a-3）

a+3) a 2+4a+5)(a+1)+(a 2+9)(a-3) =(a+3)(a 3-1+a 2-1+9a-9)=(a+3)((a-1)(a 2+a+1)+a+1+9)=(a+3)(a-1)(a 2+2a+11) Finally, bring x+3=a in.