Question

Phân tích thành nhân tử:

a) x³+y³+z³-3xyz

b) 49(y-4)²-9y²-36y-36

Answer 1

a) \(x^3+y^3+z^3-3xyz=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\)

\(=\left(x+y+z\right)\left[\left(x+y\right)^2-\left(x+y\right)z+z^2\right]-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+y^2+z^2+2xy-xz-yz\right)-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-xz\right)\)

b)  \(49\left(y-4\right)^2-9y^2-36y-36\)

\(=49\left(y-4\right)^2-\left(3y+6\right)^2\)

\(=\left[7\left(y-4\right)-\left(3y+6\right)\right]\left[7\left(y-4\right)+\left(3y+6\right)\right]\)

\(=\left(4y-34\right)\left(10y-22\right)=4\left(2y-17\right)\left(5y-11\right)\)