Đáp án+Giải thích các bước giải:
`4) (x+1)(x+2)(x+3)(x+4)+1`
`=[(x+1)(x+4)][(x+2)(x+3)]+1`
`=(x^2 + 5x +4)(x^2 + 5x +6)+1`
`=[(x^2 + 5x +5)-1][(x^2 + 5x +5)+1]`
`=(x^2 + 5x +5)^2 - 1+1`
`=(x^2 + 5x +5)^2`
`5) (x+1)(x+3)(x+5)(x+7)+15`
`= [ (x+1)(x+7)] [ (x+3)(x+5)] + 15`
`= (x^2 + 8x + 7)(x^2 + 8x+15) + 15`
`= [ (x^2 + 8x + 11) - 4][ (x^2+8x + 11) + 4] + 15`
`= (x^2 +8x+11)^2 - 4^2 + 15`
`= (x^2+8x+11)^2 - 1^2`
`= (x^2+8x+11-1)(x^2+8x+11+1)`
`= (x^2+8x+10)(x^2+8x+12)`
`=(x^2 + 8x + 10)[x(x+6)+2(x+6)]`
`=(x^2 + 8x + 10)(x+6)(x+2)`
`6) (x^2+x)^2 +4x^2 +4x -12`
`=(x^2+x)^2 + 4(x^2+x) - 12`
`=(x^2+x)^2 +2.(x^2+x).2+2^2 - 16`
`=(x^2+x+2)^2 - 4^2`
`=(x^2 +x+2-4)(x^2 + x + 2 +4)`
`=(x^2 + x - 2)(x^2 + x +6)`
`=(x-1)(x+2)(x^2 + x +6)`
`7) (x^2+x+1)(x^2+x+2)-12`
`=[(x^2 + x + 1,5) - 0,5][(x^2+x+1,5)+0,5] - 12`
`=(x^2 + x + 1,5)^2 - (0,5)^2 - 12`
`=(x^2+x+1,5)^2 - (49)/4`
`=(x^2+x+1,5)^2 - (3,5)^2`
`=(x^2 + x + 1,5 -3,5)(x^2 +x+1,5 + 3,5)`
`=(x^2 + x -2)(x^2 +x+5)`
`8) (x-1)(x+2)(x+3)(x+6) - 20`
`=[(x-1)(x+6)][(x+2)(x+3)]-20`
`=(x^2 + 5x - 6)(x^2 + 5x +6) - 20`
`=(x^2 + 5x)^2 - 6^2 - 20`
`=(x^2 + 5x)^2 - 56`
`=(x^2 + 5x)^2 - (2\sqrt{14})^2`
`= (x^2 + 5x + 2\sqrt{14})(x^2 + 5x - 2\sqrt{14})`
