Đáp án:
`a)`
` (x+1)(x+2)(x+3)(x+4) -24 = [(x+1)(x+4)][(x+2)(x+3)] -24 = (x^2 +5x +4)(x^2+5x+6)-24`
Đặt ` t = x^2 +5x +5`
` =>(x^2 +5x +4)(x^2+5x+6)-24= (t-1)(t+1) - 24 = t^2 - 1 - 24 = t^2 -25 = (t-5)(t+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)`
`b)`
Đặt ` x^2 + 4x + 8 = y` ta có
` (x^2+4x+8)^2 +3x(x^2+4x+8) +2x^2 = y^2 + 3xy + 2x^2 = y^2 +xy + 2xy + 2x^2 = y(y+x) +2x(y+x) = (y+2x)(y+x)`
` = ( x^2 +4x +8 + 2x)(x^2+4x+8+x) = [ x(x+4) +2(x+4)] (x^2+5x+8) = (x+2)(x+4)(x^2+5x+8)`
Bài `2`
` a) x^4+ 4y^4 = (x^4 + 4x^2y^2 + 4y^4) - 4xy^2 = (x^2 +2y^2)^2 - 4x^2y^2 = (x^2+ 2y^2)^2 - (2xy)^2`
` = (x^2 +2y^2 - 2xy)(x^2 + 2y^2 + 2xy)`
`b) x^5 + x -1 = x^5 + (x^4-x^4) -(x^3-x^3) - (x^2-x^2) -1 = x^5 +x^4 - x^2 -x^4 -x^3 -x + x^3 +x^2 -1`
`= x^2(x^3 +x^2-1) - x(x^3+x^2-1) + (x^3 +x^2-1) = (x^2 -x +1)(x^3 + x^2-1)`
`c) x^4 + 64 = (x^2)^2 +16x^2 + 8^2 - 16x^2 = (x^2 + 8)^2 - (4x)^2 = (x^2 -4x +8)(x^2+4x+8)`
