①(a-b)²-1 ②36x²y²-25 ③49-25a² ④16(a-b)

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  • ①(a-b)²-1

    =(a-b+1)(a-b-1)

    ②36x²y²-25

    =(6xy+5)(6xy-5)

    ③49-25a²

    =(7+5a)(7-5a)

    ④16(a-b)²-25(a+b)²

    =[4(a-b)+5(a+b)][4(a-b)-5(a+b)]

    =[4a-4b+5a+5b][4a-4b-5a-5b]

    =(9a+b)(-a-9b)

    =-(9a+b)(a+9b)

    ⑤x的四次方-x²

    =x²(x²-1)

    =x²(x+1)(x-1)

    ⑥负二分之一a²+2b²

    =2b²-a²/2

    =(4b²-a²)/2

    =(2b+a)(2b-a)/2

    ⑦x的三次方-4x

    =x(x²-4)

    =x(x+2)(x-2)

    ⑧x的四次方-1

    =(x²+1)(x²-1)

    =(x²+1)(x+1)(x-1)

    ⑨负九分之一x²+81y²

    =81y²-x²/9

    =(9y+x/3)(9y-x/3)

    ⑩(a-1)+b²(1-a)

    =(a-1)-b²(a-1)

    =(a-1)(1-b²)

    =(a-1)(1+b)(1-b)