Đáp án:
`(x + 1)(x + 3)(x + 5)(x + 7) + 15`
`= [(x + 1)(x + 7)][(x + 3)(x + 5)] + 15`
`= (x^2 + 7x + x + 7)(x^2 + 5x + 3x + 15) + 15`
`= (x^2 + 8x + 7)(x^2 + 8x + 15) + 15`
Đặt `x^2 + 8x = a`, ta được:
`(a + 7)(a + 15) + 15`
`=a^2 + 15a + 7a + 105 + 15`
`= a^2 + 22a + 120`
`= a^2 + 10a + 12a + 120`
`= a(a + 10) + 12(a + 10)`
`= (a + 10)(a + 12)`
`= (x^2 + 8x +10)(x^2 + 8x + 12)`
`=(x^2 + 8x + 10)(x^2 + 2x + 6x + 12)`
`= (x^2 + 8x + 10)[x(x + 2) + 6(x + 2)]`
`= (x^2 + 8x + 10)(x + 2)(x + 6)`
Học tốt
