Question

Rút gọn biểu thức:

a) (x - 2)(x + 2)(x² + 4) - (x² - 3)(x²+3)

b) (a + b + c)²(b + c - a)² + (c + a - b)² + (a + b - c)²

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

d) (x + 1)⁴ - 6(x + 1)² - (x² - 2)(x² + 2)

Answer 1

a) (x - 2)(x + 2)(x² + 4) - (x² - 3)(x²+3)
= (x² - 4)(x² + 4) - (x² - 3)(x²+3)

= x⁴-16-x⁴+9

= -7

Answer 2

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

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

\(=\left(x^4-16\right)-\left(x^4-9\right)\)

\(=x^4-16-x^4+9\)

\(=-7\)

Answer 3

c: \(=x^3-6x^2+12x-8-x^3-1+6x^2-12x+6\)

\(=-3\)

d: \(=x^4+4x^3+6x^2+4x+1-6x^2-12x-6-x^4+4\)

\(=4x^3-8x-1\)