Question

Phân tích đa thứ thành nhân tử

a)  4(x+y+z)^2-9(x-y-z)^2

b)  25(x-3y)^2-4(x+3y)^2

Answer 1

  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.

Answer 2

thks bn nha