SOLUTION: Factoring : a)x^4+(x-4)^4-82 b)(x^2-a)^2-6x^2+4x+2a Help me ! Thanks

Algebra ->  Rational-functions -> SOLUTION: Factoring : a)x^4+(x-4)^4-82 b)(x^2-a)^2-6x^2+4x+2a Help me ! Thanks      Log On


   

Question 1120660: Factoring :
a)x^4+(x-4)^4-82
b)(x^2-a)^2-6x^2+4x+2a
Help me ! Thanks
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
x%5E4%2B%28x-4%29%5E4-82
x%5E4%2B%28x-4%29%5E2%2A%28x-4%29%5E2-82
x%5E4%2B%28x%5E2-8x%2B16%29%2A%28x%5E2-8x%2B16%29-82
x%5E4%2Bx%5E4-8x%5E3%2B16x%5E2-8x%5E3%2B64x%5E2-128x%2B16x%5E2-128x%2B256-82
x%5E4%2Bx%5E4+-+16+x%5E3+%2B+96+x%5E2+-+256+x+%2B+256-82
2x%5E4-16x%5E3%2B96x%5E2+-+256+x+%2B174
2%28x%5E4-8x%5E3%2B48x%5E2-128x%2B87%29
2%28x%5E4-4x%5E3%2B29x%5E2-4x%5E3%2B16x%5E2-116x%2B3x%5E2-12x%2B87%29
2%28%28x%5E4-4x%5E3%2B29x%5E2%29-%284x%5E3-16x%5E2%2B116x%29%2B%283x%5E2-12x%2B87%29%29
2%28x%5E2%28x%5E2-4x%2B29%29-4x%28x%5E2-4x%2B29%29%2B3%28x%5E2-4x%2B29%29%29
2%28x%5E2-4x%2B3%29%28x%5E2+-+4x+%2B+29%29
2%28x%5E2-x-3x%2B3%29%28x%5E2+-+4x+%2B+29%29
2%28%28x%5E2-x%29-%283x-3%29%29%28x%5E2+-+4x+%2B+29%29
2%28x%28x-1%29-3%28x-1%29%29%28x%5E2+-+4x+%2B+29%29
2+%28x+-+1%29+%28x+-+3%29+%28x%5E2+-+4+x+%2B+29%29


2.
%28x%5E2-a%29%5E2-6x%5E2%2B4x%2B2a
x%5E4-2ax%5E2%2Ba%5E2-6x%5E2%2B4x%2B2a ... write -2ax%5E2 as -ax%5E2-ax%5E2, and -6x%5E2 as -2x%5E2-4x%5E2, add 2x%5E3 and -2x%5E3, add 2ax and -2ax,
x%5E4-ax%5E2-2ax%2B2ax+-ax%5E2+%2Ba%5E2-2x%5E2-4x%5E2%2B4x%2B2a+%2B2x%5E3-2x%5E3...rearrange
a%5E2-ax%5E2+%2B2ax+-ax%5E2+%2Bx%5E4-2x%5E3+-2ax%2B2x%5E3-4x%5E2+%2B2a-2x%5E2%2B4x ...group
...factor

%28a+-+x%5E2+-+2+x+%2B+2%29+%28a+-+x%5E2+%2B+2+x%29