Đáp án:
`1, (x^2 + 4x + 8)^2 + 3x(x^2 + 4x + 8) + 2x^2`
Đặt `x^2 + 4x + 8 = a`, ta được:
`a^2 + 3ax + 2x^2`
`= a^2 + ax + 2ax + 2x^2`
`= (a^2 + ax) + (2ax + 2x^2)`
`= a(a + x) + 2x(a + 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(x + 2) + 4(x + 2)]`
`= (x^2 + 5x + 8)(x + 2)(x + 4)`
`2, (x^2 + x)^2 + 5y(x^2 + x) + 6y^2`
Đặt `x^2 + x = b`, ta được:
`b^2 + 5yb + 6y^2`
`= b^2 + 2yb + 3yb + 6y^2`
`= (b^2 + 2yb) + (3yb + 6y^2)`
`= b(b + 2y) + 3y(b + 2y)`
`= (b + 2y)(b + 3y)`
`= (x^2 + x + 2y)(x^2 + x + 3y)`
