Question

Phân tích đa thức thành nhân tử

a) 25.(x+2y)²-16.(2x-y)²

b) 0,25.(x-2y)²-4.(x+y)²

c) \(\dfrac{4}{9}\).(x-3y)²-0,04.(x+y)²

d) -25x²+30x-9

Answer 1

a: \(=\left(5x+10y\right)^2-\left(8x-4y\right)^2\)

\(=\left(5x+10y-8x+4y\right)\left(5x+10y+8x-4y\right)\)

\(=\left(-3x+14y\right)\left(13x+6y\right)\)

b: \(=\left(\dfrac{1}{2}x-y\right)^2-\left(2x+2y\right)^2\)

\(=\left(\dfrac{1}{2}x-y-2x-2y\right)\left(\dfrac{1}{2}x-y+2x+2y\right)\)

\(=\left(-\dfrac{3}{2}x-3y\right)\left(\dfrac{5}{2}x+y\right)\)

c: \(=\left(\dfrac{2}{3}x-2y\right)^2-\left(\dfrac{1}{5}x+\dfrac{1}{5}y\right)^2\)

\(=\left(\dfrac{2}{3}x-2y-\dfrac{1}{5}x-\dfrac{1}{5}y\right)\left(\dfrac{2}{3}x-2y+\dfrac{1}{5}x+\dfrac{1}{5}y\right)\)

\(=\left(\dfrac{7}{15}x-\dfrac{11}{5}y\right)\left(\dfrac{13}{15}x-\dfrac{9}{5}y\right)\)