Question

Chứng minh rằng giá trị các biểu thức sau k phụ thuộc vào biến:

a) (1/3+2x)(4x²-2/3x+1/9)-(8x³-1/27)

b) (x-1)³-(x-1)(x²+x+1)-3(1-x)x

c) y(x²-y²)(x²+y²)-y(x⁴-y⁴)

giải jup mk vs ạk

Answer 1

a: \(\left(2x+\dfrac{1}{3}\right)\left(4x^2-\dfrac{2}{3}x+\dfrac{1}{9}\right)-\left(8x^3-\dfrac{1}{27}\right)\)

\(=8x^3+\dfrac{1}{27}-8x^3+\dfrac{1}{27}=\dfrac{2}{27}\)

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

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

\(=-3x^2+3x+3x^2-3x=0\)

c: \(=y\left(x^4-y^4\right)-y\left(x^4-y^4\right)=0\)