Question

thực hiện phép tính :

a/(2x+3y)²

b/(x²+\(\dfrac{2}{5}\)y).(x² -\(\dfrac{2}{5}\)y)

c/(x-3y).(x²+3xy+9y²)

d/(x+2y+z).(x+2y-z)

e/(x²-3).(x⁴+3x²+9)

Answer 1

a) \(\left(2x+3y\right)^2=4x^2+12xy+9y^2\)

b) \(\left(x^2+\dfrac{2}{5}y\right)\left(x^2-\dfrac{2}{5}y\right)=\left(x^2\right)^2-\left(\dfrac{2}{5}y\right)^2\)

\(=x^4-\dfrac{4}{25}y^2\)

c) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)=\left(x-3y\right)\left[x^2+3y.x+\left(3y\right)^2\right]\)

\(=x^3-\left(3y\right)^3=x^3-27y^3\)

d) \(\left(x+2y+z\right)\left(x+2y-z\right)=\left(x+2y\right)^2-z^2=x^2+4xy+4y^2-z^2\)

e) \(\left(x^2-3\right)\left(x^4+3x^2+9\right)=\left(x^2-3\right)\left[\left(x^2\right)^2+3.x^2+3^2\right]\)

\(=\left(x^2\right)^3-3^3=x^6-27\)