分解因式:(1).(x+2)的3次方-(x-2)的3次方 (2).1\2x的4次方-8 (3).x的4次方+7x的2次方
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  • (1).(x+2)的3次方-(x-2)的3次方

    =(x+2-x+2)[(x+2)²+(x+2)(x-2)+(x-2)²]

    =4(3x²+4)

    (2).12x的4次方-8

    =1/2(x的4次方-16)

    =1/2(x²+4)(x²-4)

    =1/2(x²+4)(x+2)(x-2)

    (3).x的4次方+7x的2次方-8

    =(x²+8)(x²-1)

    =(x²+8)(x+1)(x-1)

    (4)a的4次方-a的3次方+a的2次方-a

    =a³(a-1)+a(a-1)

    =a(a-1)(a²+1)

    (5).4a的2次方-9b的2次方+c的2次方-4ac

    =(2a-c)²-(3b)²

    =(2a-c+3b)(2a-c-3b)

    (6)(ax+by)的2次方+(bx-ay)的2次方

    =a²x²+2abxy+b²y²+b²x²-2abxy+a²y²

    =a²x²+a²y²+b²y²+b²x²

    =a²(x²+y²)+b²(x²+y²)

    =(x²+y²)(a²+b²)

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