Question

Thực hiện phép tính :

a) (x-1)(x+1)(x+2)

b) \(\dfrac{1}{2}x^2y^2\left(2x+y\right)\left(2x-y\right)\)

c)\(\left(x-\dfrac{1}{2}\right)\left(x+\dfrac{1}{2}\right)\left(4x-1\right)\)

Answer 1

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

b) \(\dfrac{1}{2}x^2y^2\left(2x+y\right)\left(2x-y\right)\\ =\dfrac{1}{2}x^2y^2\left(4x^2-y^2\right)\\ =2x^4y^2-\dfrac{1}{2}x^2y^4\)

c) \(\left(x-\dfrac{1}{2}\right)\left(x+\dfrac{1}{2}\right)\left(4x-1\right)\\ =\left(x^2-\dfrac{1}{4}\right)\left(4x-1\right)\\ =4x^3-x^2-x+\dfrac{1}{4}\)

Answer 2

a) \(\left(x-1\right)\left(x+1\right)\left(x+2\right)\)

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

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

b) \(\dfrac{1}{2}x^2y^2\left(2x+y\right)\left(2x-y\right)\)

\(=\dfrac{1}{2}x^2y^2\cdot\left(4x^2-y^2\right)\)

\(=2x^4y^2-\dfrac{1}{2}x^2y^4\)

c) \(\left(x-\dfrac{1}{2}\right)\left(x+\dfrac{1}{2}\right)\left(4x-1\right)\)

\(=\left(x^2-\dfrac{1}{4}\right)\cdot\left(4x-1\right)\)

\(=4x^3-x^2-x+\dfrac{1}{4}\)

Answer 3

a) (x-1)(x+1)(x+2)

=(x²-1)(x+2)

=x³+2x²-x-2

b) \(\dfrac{1}{2}x^2y^2\left(2x+y\right)\left(2x-y\right)\)

\(\Leftrightarrow\dfrac{1}{2}x^2y^2\left(4x^2-y^2\right)\)

\(\Leftrightarrow2x^4y^2-\dfrac{1}{2}x^2y^4\)

c) \(\left(x-\dfrac{1}{2}\right)\left(x+\dfrac{1}{2}\right)\left(4x-1\right)\)

\(\Leftrightarrow\left(x^2-\dfrac{1}{4}\right)\)\(\left(4x-1\right)\)

\(\Leftrightarrow4x^3-x^2-x+\dfrac{1}{4}\)