Đáp án: + Giải thích các bước giải:
` a) (x+2)(x+3)(x-7)(x-8)-144`
`=(x+2)(x-7)(x+3)(x-8)-144`
`=(x^2-7x+2x-14)(x^2-8x+3x-24)-144`
`=(x^2-5x-14)(x^2-5x-24)-144`
`=(x^2-5x-14)(x^2-5x-14-10)-144`
Đặt `a=x^2-5x-14 `ta được :
`a.(a-10)-144`
`=a^2-10a-144`
`=a^2-18a+8a-144`
`=a(a-18)+8(a-18)`
`=(a+8)(a-18)`
Hay `(x^2-5x-14+8)(x^2-5x-14-18)`
`=(x^2-5x-6)(x^2-5x-32)`
`=(x^2+x-6x-6)(x^2-5x-32)`
`=[x(x+1)-6(x+1)](x^2-5x-32)`
`=(x-6)(x+1)(x^2-5x-32)`
`b)x^4+324`
`=x^4+324+36x^2-36x^2`
`=(x^2+18)^2-36x^2`
`=(x^2+18-6x)(x^2+18x+6x)`
`c) x^40 +2x^20 +9`
`=x^40 +2x^20 +4x^20 +9 -4x^20`
`=x^40 +6x^20 +9 -4x^20`
`=(x^20+3)^2- (2x^10)^2`
`=(x^20 + 3-2x^10 )(x^20 + 3 + 2x^10 )`
`d)ab(a-b)-bc(b-c)-ca(c-a)`
`=ab(a-b)-bc(b-c)-ca(c-a)`
`=a^2b-ab^2-b^2c+bc^2-c^2a+ca^2`
`=bc^2-^2c-abc-ab^2-c^2a+abc+ca^2+a^2b`
`=b(c^2-bc-ac-ab)-a(c^2-bc-ac-ab)`
`=(b-a)(c^2-bc-ac-ab)`
