Question

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

a) y.(x²-y²).(x²+y²)-y.(x⁴-y⁴)

b) (\(\dfrac{1}{3}\)+2x).(4x²-\(\dfrac{2}{3}\)x+\(\dfrac{1}{9}\))-(8x³-\(\dfrac{1}{27}\))

c) (x-1)³-(x-1).(x²+x+1)-3.(1-x).x

Answer 1

a: Ta có: \(y\left(x^2-y^2\right)\cdot\left(x^2+y^2\right)-y\left(x^4-y^4\right)\)

\(=y\left(x^4-y^4\right)-y\left(x^4-y^4\right)\)

=0

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

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

\(=\dfrac{2}{27}\)

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

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

=0