Đáp án:
Bài 1 :
$a) (2+xy)^2 = (2+xy)(2+xy) = 4 +2xy+2xy+x^2y^2 = 4+4xy+x^2y^2$
$b) (5-3x)^2 = (5-3x)(5-3x) = 25 -15x-15x +9x^2 = 25-30x+9x^2$
$c) (5-x^2)(5+x^2) = 25 +5x^2-5x^2 -x^4 = 25 -x^5$
$d) (5x-1)^3 = (5x-1)(5x-1)^2 = (5x-1)(25x^2-10x+1) = 125x^3 -50x^2+5x-25x^2+10x-1 = 125x^3 -75x^2+15x -1$
$e) (2x-y)(4x^2+2xy+y^2) = 8x^3 +4x^2y+2xy^2 -4x^2y -2xy^2-y^3 = 8x^3-y^3$
$f) (x+3)(x^2-3x+9) = x^3 -3x^2+9x+3x^2-9x+27 = x^3 +27$
Bài 2 :
$a) (x+3)(x^2-3x+9) - (54+x^3) = (x^3-3x^2+9x+3x^2-9x+27) - (54+x^3) = x^3 +27 - 54-x^3 = -27$
$b) (2x+y)((4x^2-2xy+y^2) - (2x-y)(4x^2+2xy+y^2) = (8x^3-4x^2y+2xy^2-4x^2y-2xy^2+y^3) - (8x^3+4x^2y+2xy^2-4x^2y-2xy^2-y^3) = 8x^3 +y^3 - (8x^3-y^3) = 8x^3+y^3 -8x^3+y^3 =2y^3$
