Question

1) Triển khai

a) 9x² - \(\dfrac{1}{25}\)

b) x⁶ - y⁶

 

Answer 1

\(a,9x^2-\dfrac{1}{25}=\left(3x\right)^2-\left(\dfrac{1}{5}\right)^2=\left(3x-\dfrac{1}{5}\right)\left(3x+\dfrac{1}{5}\right)\)

\(b,x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3-y^3\right)\left(x^3+y^3\right)\\ =\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)

Answer 2

a) \(9x^2-\dfrac{1}{25}=\left(3x\right)^2-\left(\dfrac{1}{5}\right)^2=\left(3x-\dfrac{1}{5}\right)\left(3x+\dfrac{1}{5}\right)\)

b) \(x^6-y^6=\left(x^2\right)^3-\left(y^2\right)^3=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)=\left(x-y\right)\left(x+y\right)\left[\left(x^2+y^2\right)^2-2x^2y^2+x^2y^2\right]\)

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