Rút gọn biểu thức: a) (a^2+a-1)(a^2-a+1) b) (a+2)(a-2))a^2+2a+4)(a^2-2a+4) c)(2+3y)^2-(2x-3y)^2-12xy d) (x+1)^3-(x-1)^3-(x^3-1)-)x-1)(x^2+x+1) Mn giúp

Đáp án:

 $a) a^4-a^2+2a-1\\
b) (a^2-4)^3\\
c)4+12y-4x^2\\
d) -2x^3+6x^2+4$

Giải thích các bước giải:

 $a) (a^2+a-1)(a^2-a+1)\\
=(a^2)^2-(a-1)^2\\
=a^4-a^2+2a-1\\
b) (a+2)(a-2)(a^2+2a+4)(a^2-2a+4)\\
=(a^2-4).(a+2)^2.(a-2)^2\\
=(a^2-4).(a^2-4)^2\\
=(a^2-4)^3\\
c) (2+3y)^2-(2x-3y)^2-12xy\\
=4+2.2.3y+9y^2-(4x^2-2.2x.3y+9y^2)-12xy\\
=4+12y+9y^2-4x^2+12xy-9y^2-12xy\\
=4+12y-4x^2\\
d) (x+1)^3-(x-1)^3-(x^3-1)-(x-1)(x^2+x+1)\\
=x^3+3x^2+3x+1-(x^3-3x^2+3x-1)-x^3+1-(x^3-1)\\
=x^3+3x^2+3x+1-x^3+3x^2-3x+1-x^3+1-x^3+1\\
=(x^3-x^3-x^3-x^3)+(3x^2+3x^2)+(3x-3x)+1+1+1+1\\
=-2x^3+6x^2+4$