Đáp án:

`b)(x²+3x+1)²`

`c)(x²+x+5)(x+2)(x-1)`

`d)(x+2)(x+4)(x²+5x+8)`

`e)x(x²+5x+10)(x+5)`

Giải thích các bước giải:

`b)x(x+1)(x+2)(x+3)+1`

`=[x(x+3)][(x+1)(x+2)]+1`

`=(x²+3x)(x²+2x+x+2)+1`

`=(x²+3x)(x²+3x+2)+1`

Đặt `x²+3x=a`, khi đó ta được:

       `a(a+2)+1`

    `=a²+2a+1`

    `=(a+1)²`

    `=(x²+3x+1)²`

`c)(x²+x+1)(x²+x+2)-12`

Đặt `x²+x+1=a`, khi đó ta được:

       `a(a+1)-12`

    `=a²+a-12`

    `=a²+4a-3a-12`

    `=a(a+4)-3(a+4)`

    `=(a+4)(a-3)`

    `=(x²+x+1+4)(x²+x+1-3)`

    `=(x²+x+5)(x²+x-2)`

    `=(x²+x+5)(x²+2x-x-2)`

    `=(x²+x+5)[x(x+2)-(x+2)]`

    `=(x²+x+5)(x+2)(x-1)`

`d)(x^2+4x+8)^2+3x(x²+4x+8)+2x²`

Đặt `x²+4x+8=a`, khi đó ta được:

       `a²+3ax+2x²`

    `=a²+2ax+ax+2x²`

    `=a(a+2x)+x(a+2x)`

    `=(a+2x)(a+x)`

    `=(x²+4x+8+2x)(x²+4x+8+x)`

    `=(x²+6x+8)(x²+5x+8)`

    `=(x²+2x+4x+8)(x²+5x+8)`

    `=[x(x+2)+4(x+2)](x²+5x+8)`

    `=(x+2)(x+4)(x²+5x+8)`

`e)(x+1)(x+2)(x+3)(x+4)-24`

`=[(x+1)(x+4)][(x+2)(x+3)]-24`

`=(x²+4x+x+4)(x²+3x+2x+6)-24`

`=(x²+5x+4)(x²+5x+6)-24`

Đặt `x²+5x+5=a`, khi đó ta được:

        `(a-1)(a+1)-24`

    `=a²-1-24`

    `=a²-25`

    `=a²-5²`

    `=(a+5)(a-5)`

    `=(x²+5x+5+5)(x²+5x+5-5)`

    `=(x²+5x+10)(x²+5x)`

    `=x(x²+5x+10)(x+5)`

Đáp án:

 `b, x(x + 1)(x +2)(x + 3) + 1`

`= [x(x + 3)][(x + 1)(x + 2)] + 1`

`= (x^2 + 3x)(x^2 + 3x + 2) + 1`

Đặt `x^2 + 3x + 1 =a`, ta được:

`(a - 1)(a +1) + 1`

`= a^2 - 1 + 1`

`= a^2`

`= (x^2 + 3x + 1)^2`

`c, (x^2 + x + 1)(x^2 + x + 2) - 12`

Đặt `x^2 + x = a`, ta được:

`(a + 1)(a + 2)-12`

`= a^2 + 2a + 1 + 2 - 12`

`= a^2 + 3a - 10`

`= a^2 - 2a + 5a - 10`

`= (a^2 - 2a) + (5a - 10)`

`= a(a - 2) + 5(a - 2)`

`= (a -2 )(a + 5)`

`= (x^2 + x - 2)(x^2 + x + 5)`

`= [(x^2 - x) + (2x - 2)](x^2 + x + 5)`

`= [x(x - 1) + 2(x - 1)](x^2 + x + 5)`

`= (x - 1)(x + 2)(x^2 + x + 5)`

`d, (x^2 + 4x + 8)^2 + 3x(x^2 + 4x + 8) + 2x^2`

Đặt `x^2 + 4x + 8 = a`, ta được:

`a^2 + 3xa + 2x^2`

`= a^2 + 2ax + x^2 + ax + x^2`

`= (a^2 + 2ax + x^2) + (ax + x^2)`

`= (a + x)^2 + x(a + x)`

`= (a + x)(a + x + x)= (a + x)(a + 2x)`

`= (x^2 + 4x + 8 + x)(x^2 + 4x + 8 + 2x)`

`= (x^2 + 5x + 8)(x^2 + 6x + 8)`

`= (x^2 + 5x + 8)(x^2 +2x + 4x + 8)`

`= (x^2 + 5x + 8)[(x^2 + 2x) + (4x + 8)]`

`= (x^2 + 5x + 8)[x(x + 2) + 4(x + 2)`

`= (x^2 + 5x + 8)(x + 2)(x + 4)`

`e, (x  + 1)(x + 2)(x + 3)(x + 4) - 24`

`= [(x + 1)(x + 4)][(x + 2)(x + 3)] - 24`

`= (x^2 + 4x + x + 4)(x^2 + 3x + 2x + 6) - 24`

`= (x^2 + 5x + 4)(x^2 + 5x + 6) - 24`

Đặt `x^2 + 5x + 5 = a`, ta được:

`(a - 1)(a + 1) - 24`

`= a^2 - 1 - 24`

`= a^2 - 25 =a^2 - 5^2`

`= (a - 5)(a + 5)`

`= (x^2 + 5x + 5 - 5)(x^2 + 5x + 5 + 5)`

`= (x^2 + 5x)(x^2 + 5x + 10)`

`= x(x + 5)(x^2 + 5x + 10)`