\(1.A=\left(x-2y\right)^3-\left(x+2y\right)^3+12x^2y-xy\\ =x^3-3x^2.2y+3x\cdot\left(2y\right)^2-\left(2y\right)^3-\left[x^3+3x^2\cdot2y+3x\cdot\left(2y\right)^2+\left(2y\right)^3\right]+12x^2y-xy\)
\(=x^3-6x^2y+12xy^2-8y^3-x^3-6x^2y-12xy^2-8y^3+12x^2y-xy\\ =xy-16y^3\)
2 . Tìm x :
\(a)\left(2x-3\right)^2-\left(x+2\right)^2=0\\ \left[\left(2x-3\right)-\left(x+2\right)\right]\cdot\left[\left(2x-3\right)+\left(x+2\right)\right]=0\\ \left(2x-3-x-2\right)\cdot\left(2x-3+x+2\right)=0\\ \left(x-5\right)\left(3x-1\right)=0\\ 4x-x-15x+5=0\\ -18x=-5\Rightarrow x=\dfrac{5}{18}\)
\(b)\left(x-3\right)^3=x\cdot\left(x^2-9x+2\right)\\ x^3-9x^2+27x-27=x^3-9x^2+2x\\ \Leftrightarrow27x-27=2x\\ \Leftrightarrow27x-2x=27\\ \Leftrightarrow25x=27\\ \Leftrightarrow x=\dfrac{27}{25}\)
\(c)36x^2-49=0\\ \Leftrightarrow36x^2=49\\ \Leftrightarrow x^2=\dfrac{49}{36}\\ \Leftrightarrow x^2=\left(\pm\dfrac{7}{6}\right)^2\\ \Rightarrow x=\pm\dfrac{7}{6}\)