Question

Rút gọn các biểu thức sau:

a) (x² - 1)³ - (x⁴ + x² + 1) (x² - 1)

b) (x⁴ - 3x² +9) (x² + 3) - (3 + x²)³

c) (x - 3)³ - (x - 3) (x² + 3x + 9) + 6 (x + 1)²

Answer 1

a) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2-1\right)\)

\(=x^6-3x^4+3x^2-1-x^6+1\)

\(=-3x^4+3x^2\)

b) \(\left(x^4-3x^2+9\right)\left(x^2+3\right)-\left(3+x^2\right)^3\)

\(=x^6+27-27-27x^2-9x^4-x^6\)

\(=-27x^2-9x^4\)

c) \(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2\)

\(=x^3-9x^2+27x-27-x^3+27+6x^2+12x+1\)

\(=-3x^2+39x+1\)

Answer 2

a: \(=x^6-3x^4+3x^2-1-\left(x^6-1\right)\)

\(=-3x^4+3x^2\)

b: \(=x^6+27-\left(x^6+3x^4+9x^2+27\right)\)

\(=x^6+27-x^6-3x^4-9x^2-27=-3x^4-9x^2\)

c: \(=x^3-9x^2+27x-27-x^3+27+6\left(x^2+2x+1\right)\)

\(=-9x^2+27x+6x^2+12x+6=-3x^2+39x+6\)