Question

Rút gọn biểu thức:

a) (x 2 – 2x + 2)(x 2 – 2)(x 2 + 2x + 2)(x 2 + 2)

b) (x + 1)² – (x – 1)² + 3x 2 – 3x(x + 1)(x – 1)

c) (2x + 1)² + 2(4x 2 – 1) + (2x – 1)²

d) (m + n)² – (m – n)² + (m – n)(m + n) 

e) (3x + 1)² – 2(3x + 1)(3x + 5) + (3x + 5)²

Answer 1

a: Ta có: \(\left(x^2-2x+2\right)\left(x^2-2\right)\left(x^2+2x+2\right)\left(x^2+2\right)\)

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

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

\(=\left(x^4-4\right)\cdot\left(x^4+4\right)\)

\(=x^8-16\)

b: Ta có: \(\left(x+1\right)^2-\left(x-1\right)^2+3x^2-3x\left(x+1\right)\left(x-1\right)\)

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

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

\(=-3x^3+3x^2+7x\)