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`a,`
`(a^2 +a+1)(a^2 +a+2)-12`
Đặt `a^2+a+1=x`
`= x (x+1)-12`
`=x^2 +x-12`
`= x^2 +2 . x . 1/2 + 1/4 - 1/4 - 12`
`= x^2+ 2 . x . 1/2 + (1/2)^2 -49/4`
`= (x+1/2)^2 - (7/2)^2`
`= (x+1/2 - 7/2) (x+1/2 +7/2)`
`= (x-3) (x+4)`
`= (a^2 +a+1-3) (a^2 +a+1+4)`
`= (a^2 +a - 2) (a^2 +a+5)`
`= (a^2 +2a-a -2) (a^2 +a+5)`
`= [(a^2 +2a)-(a+2)] (a^2 +a+5)`
`= [a (a+2) - (a+2)] (a^2+a+5)`
`= (a+2)(a-1) (a^2 +a+5)`
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`b,`
`(a-2)(a-4) (a-6)(a-8) +16`
`= [(a-2)(a-8)] [(a-4)(a-6)]+16`
`= (a^2 - 8a - 2a +16) (a^2 - 6a -4a+24)+16`
`= (a^2 - 10a + 16) (a^2 - 10a +24)+16`
Đặt `a^2 - 10a +16=x`
`= x (x+8) +16`
`= x^2 +8x +16`
`=x^2 +2 . x . 4 + 4^2`
`= (x+4)^2`
`= (a^2 - 10a +16+4)^2`
`= (a^2 -10a+20)^2`
