Question 1120660

1.

{{{x^4+(x-4)^4-82}}}

{{{x^4+(x-4)^2*(x-4)^2-82}}}

{{{x^4+(x^2-8x+16)*(x^2-8x+16)-82}}}

{{{x^4+x^4-8x^3+16x^2-8x^3+64x^2-128x+16x^2-128x+256-82}}}

{{{x^4+x^4 - 16 x^3 + 96 x^2 - 256 x + 256-82}}}

{{{2x^4-16x^3+96x^2 - 256 x +174}}}

{{{2(x^4-8x^3+48x^2-128x+87)}}}

{{{2(x^4-4x^3+29x^2-4x^3+16x^2-116x+3x^2-12x+87)}}}

{{{2((x^4-4x^3+29x^2)-(4x^3-16x^2+116x)+(3x^2-12x+87))}}}

{{{2(x^2(x^2-4x+29)-4x(x^2-4x+29)+3(x^2-4x+29))}}}

{{{2(x^2-4x+3)(x^2 - 4x + 29)}}}

{{{2(x^2-x-3x+3)(x^2 - 4x + 29)}}}

{{{2((x^2-x)-(3x-3))(x^2 - 4x + 29)}}}

{{{2(x(x-1)-3(x-1))(x^2 - 4x + 29)}}}

{{{2 (x - 1) (x - 3) (x^2 - 4 x + 29)}}}



2.

{{{(x^2-a)^2-6x^2+4x+2a}}}

{{{x^4-2ax^2+a^2-6x^2+4x+2a}}} ... write {{{-2ax^2}}} as {{{-ax^2-ax^2}}}, and {{{-6x^2}}} as {{{-2x^2-4x^2}}}, add {{{2x^3}}} and {{{-2x^3}}}, add {{{2ax}}} and {{{-2ax}}}, 

{{{x^4-ax^2-2ax+2ax -ax^2 +a^2-2x^2-4x^2+4x+2a +2x^3-2x^3}}}...rearrange

{{{a^2-ax^2 +2ax -ax^2 +x^4-2x^3 -2ax+2x^3-4x^2 +2a-2x^2+4x}}} ...group

{{{(a^2-ax^2 +2ax )-(ax^2 -x^4+2x^3 )-(2ax-2x^3+4x^2)+(2a-2x^2+4x )}}} ...factor

{{{a(a-x^2 +2x )- x^2(a  -x^2+2x )  - 2x(a-x^2+2x)  +2(a-x^2+2x ) }}}

{{{(a - x^2 - 2 x + 2) (a - x^2 + 2 x)}}}