因式分解16(x^2+4x+4)^2(x^2-2x+1)^2-(x^2-6x+9)^2 那位大侠帮忙看看这题怎么分解?
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因式分解16(x^2+4x+4)^2(x^2-2x+1)^2-(x^2-6x+9)^2 那位大侠帮忙看看这题怎么分解?
因式分解16(x^2+4x+4)^2(x^2-2x+1)^2-(x^2-6x+9)^2 那位大侠帮忙看看这题怎么分解?
因式分解16(x^2+4x+4)^2(x^2-2x+1)^2-(x^2-6x+9)^2 那位大侠帮忙看看这题怎么分解?
[4(x+2)(x-1)]^2-(x-3)^2
=[4(x+2)(x-1)+(x-3)][4(x+2)(x-1)-(x-3)]
=(4x^2+4x-8+x-3)(4x^2+4x-8-x+3)
=(4x^2+5x-11)(4x^2+3x-5)
16(x²+4x+4)²(x²-2x+1)²-(x²-6x+9)²
= 16[(x+2)^4][(x-1)^4] - (x-3)^4
= [2(x+2)(x-1)]²² - (x-3)²²
= {[2(x+2)(x-1)]² - (x-3)²} {[2(x...
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16(x²+4x+4)²(x²-2x+1)²-(x²-6x+9)²
= 16[(x+2)^4][(x-1)^4] - (x-3)^4
= [2(x+2)(x-1)]²² - (x-3)²²
= {[2(x+2)(x-1)]² - (x-3)²} {[2(x+2)(x-1)]² + (x-3)²}
= {[2(x+2)(x-1)] - (x-3)} {[2(x+2)(x-1)] + (x-3)} {4(x²+x-2)² + x²-6x+9}
= [2(x²+x-2) -x+3] [2(x²+x-2) +x-3] [4(x^4 +x² +4 +2x^3 -4x² -4x) +x²-6x+9]
= (2x²+x-1) (2x²+3x-7) [4(x^4 +2x^3 -3x²-4x+4) +x²-6x+9]
= (2x-1)(x+1)(2x²+3x-7) (4x^4 +8x^3 -11x²-22x+25)
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