Giải thích các bước giải:
a) a^3 - a^2x - ay -xy
b) x^3 - x + y^3 - y
=(x^3+y^3)-(x+y)
=(x+y)(x^2-xy+y^2) - (x+y)
=(x+y)(x^2-xy+y2-1)
c) 4x^2 - y^2 + 4x +1
=(4x^2+4x+1)-y^2
=[(2x)^2+2.2x.1+1^2]-y^2
=(2x+1)^2-y^2
=[(2x+1)+y][(2x+1)-y]
=(2x+1+y)(2x+1-y)
d) 5x^2 + 5xy - x- y
=(5x^2-x)+(5xy-y)
=x(5x-1)+y(5x-1)
=(5x-1)(x+y)
e)x^2 - 4z^2 + y^2 - 2xy
=(x^2-2xy+y^2) - 4z^2
=(x-y)^2 - 4z^2
=[(x-y) + 4z][(x-y) - 4z]
=(x-y - 4z)(x-y - 4z)
f) 5x^2 - 10xy +5y^2 - 20z^2
=5(x^2 - 2xy +y^2 - 4y^2)
=5[(x^2 - 2xy +y^2) - 4y^2]
=5[(x-y)^2 - 4y^2]
=5[(x-y) - 4y][(x-y)- 4y]
=5(x-y+ 4y)(x-y- 4y)
g) x^3 - x + 3x^2y + 3xy^2 + y^3 - y
=(x^3 + 3x^2y + 3xy^2 + y^3) - (x+y)
=(x+y)^3 -(x+y)
=(x+y)[(x+y)^2-1^2]
=(x+y)[(x+y)+1][(x+y)-1]
=(x+y)(x+y+1)(x+y-1)
h) (3x + 1 )^2 + (x +1 )^2
=[(3x)^2+2.3x.1+1^2]+[x^2+2.x.1+1^2]
=(9x^2+6x+1)+(x^2+2x+1)
=9x^2+6x+1+x^2+2x+1
=(9x^2+x^2)+(6x+2x)+(1+1)
=10x^2+8x+2
