Question

Phân tích các đa thức sau thành nhân tử :

a) (x+y+z)³ - x³ - y³ - z³

b) x(y² - z²) + y(z² - x²) + z(x²-y²)

c) xy(x+y) + yz(y+z) + zx (z+x) + 3xyz

d)(xy + 4)² - (2x + 2y)²

e) 2x⁴ + 7x³ +3

f) x² - 4xy + 3y²

Ai đó giúp em với ~~

Answer 1

d: \(\left(xy+4\right)-\left(2x+2y\right)^2\)

\(=\left(xy+4-2x-2y\right)\left(xy+4+2x+2y\right)\)

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

\(=\left(y-2\right)\left(x-2\right)\left(y+2\right)\left(x+2\right)\)

f: \(x^2-4xy+3y^2\)

\(=x^2-xy-3xy+3y^2\)

\(=x\left(x-y\right)-3y\left(x-y\right)\)

\(=\left(x-y\right)\left(x-3y\right)\)