Dùng hằng thức để khai triển và thu gọn:
a) (x+1) ³ – (x-1) ³ – 6(x-1)(x+1)
b) x(x-1)(x+1) – (x+1)(x ²-x+1)
c) (x-1) ³ – (x+2)(x ²-2x+4) + 3(x+4)(x-4)
d) 3x ²(x+1)(x-1) + (x ²-1) ³ – (x ²-1)(x^4+x ²+1)
e) (x^4-3x ²+9)(x ²+3) + (3-x ²) ³ – 9x ²(x ²-3)
a,x³+3x²+3x+1-(x³-3x²+3x-1)-6(x²-1)
=x³+3x²+3x+1-x³+3x²-3x+1-6x²+6
=8
b,x(x-1)(x+1) – (x+1)(x ²-x+1)
=x(x²-1)-(x³+1)
=x³-x-x³-1
=-x-1
c,(x-1) ³ – (x+2)(x ²-2x+4) + 3(x+4)(x-4)
=x³-3x²+3x-1-(x³+8)+3(x²-16)
=x³-3x²+3x-1-x³-8+3x²-48
=3x-57
d,3x ²(x+1)(x-1) + (x ²-1) ³ – (x ²-1)(x^4+x ²+1)
=3x²(x²-1)+(x^6-3x^4+3x²-1)-(x^6-1)
=3x^4-3x²+x^6-3x^4+3x²-1-x^6+1
=0
e,(x^4-3x²+9)(x²+3)+(3-x²)³-9x²(x²-3)
=(x^6+3x^4-3x^4-9x²+9x²+27)+(27-27x²+9x^4-x^6)-9x^4+27x²
=x^6+27+27-27x²+9x^4-x^6-9x^4+27x²
=54
Xin CTLHN