Giải thích các bước giải:

8/ $(x-2)(x-3)+(x-2)-1$

$=(x-2)(x-3+1)-1$

$=(x-2)^2-1$

$=(x-2-1)(x-2+1)$

$=(x-3)(x-1)$

9/ $3(x-1)+5(1-x)$

$=3(x-1)-5(x-1)$

$=-2(x-1)$

10/ $ax-2x-a^2+2a$

$=x(a-2)-a(a-2)$

$=(a-2)(x-a)$

11/ $x^4-4(x^2+5)-25$

$=(x^4-25)-4(x^2+5)$

$=(x^2-5)(x^2+5)-4(x^2+5)$

$=(x^2+5)(x^2-5-4)$

$=(x^2+5)(x^2-9)$

$=(x^2+5)(x-3)(x+3)$

12/ $5x^2+5xy-x-y$

$=5x(x+y)-(x+y)$

$=(x+y)(5x-1)$

13/ $x^3-4x^2-12x+27$

$=(x^3+27)-(4x^2+12x)$

$=(x+3)(x^2-3x+9)-4x(x+3)$

$=(x+3)(x^2-3x+9-4x)$

$=(x+3)(x^2-7x+9)$

$=\dfrac{1}{4}(x+3)(4x^2-28x+36)$

$=\dfrac{1}{4}(x+3)(4x^2-28x+49-13)$

$=\dfrac{1}{4}(x+3)[(2x-7)^2-13]$

$=\dfrac{1}{4}(x+3)(2x-7-\sqrt{13})(2x-7+\sqrt{13})$

17/ $81a^2-6bc-9b^2-c^2$

$=81a^2-(9b^2+6bc+c^2)$

$=81a^2-(3b+c)^2$

$=(9a-3b-c)(9a+3b+c)$

18/ $2x^2-12x+18+2xy-6y$

$=2(x^2-6x+9)+2y(x-3)$

$=2(x-3)^2+2y(x-3)$

$=2(x-3)(x-3+2y)$

19/ $4xy-4y^2+25-x^2$

$=25-(x^2-4xy+4y^2)$

$=25-(x-2y)^2$

$=(5-x+2y)(5+x-2y)$

20/ $x^2+4x-4y^2+8y$

$=(x^2+4x+4)-(4y^2-8y+4)$

$=(x+2)^2-(2y-2)^2$

$=(x+2-2y+2)(x+2+2y-2)$

$=(x-2y+4)(x+2y)$

21/ $x^3+2x^2y+xy^2-16x$

$=x(x^2+2xy+y^2-16)$

$=x[(x+y)^2-16]$

$=x(x+y-4)(x+y+4)$

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