a, \(4\left(x+y+z\right)^2-9\left(x-y-z\right)^2\)
\(=\left[2\left(x+y+z\right)\right]^2-\left[3\left(x-y-z\right)\right]^2\)
\(=\left[2x+2y+2z\right]^2-\left[3x-3y-3z\right]^2\)
\(=\left[\left(2x+2y+2z\right)-\left(3x-3y-3z\right)\right].\left[\left(2x+2y+2z\right)+\left(3x-3y-3z\right)\right]\)
\(=\left(-x+5y+5z\right)\left(5x-y-z\right)\)
b, \(25\left(x-3y\right)^2-4\left(x+3y\right)^2\)
\(=\left[5\left(x-3y\right)\right]^2-\left[2\left(x+3y\right)\right]^2\)
\(=\left[5x-15y\right]^2-\left[2x+6y\right]^2\)
\(=\left[5x-15y-2x-6y\right].\left[5x-15y+2x+6y\right]\)
\(=\left(3x-21y\right)\left(7x-9y\right)\)
\(=3\left(x-7y\right)\left(7x-9y\right)\)
Chúc bạn học tốt.
