Question

[sOKn0340]

Rút gọn:

a, (x-1)³ - (x+1)(x²-x+1) - (3x+1)(1-3x)

b, (x+y+z-t)(x+y-z+t)

Mọi người giải chi tiết cho mình những câu trên nha!

Cảm ơn các bạn :333

Answer 1

[Nguyễn Tấn Phát]

\(\text{a) }\left(x-1\right)^3-\left(x+1\right)\left(x^2-x+1\right)-\left(3x+1\right)\left(1-3x\right)\)

\(=\left(x^3-3x^2+3x-1\right)-\left(x^3+1\right)-\left[1-\left(3x\right)^2\right]\)

\(=x^3-3x^2+3x-1-x^3-1-1+9x^2\)

\(=6x^2+3x-3\)

\(\text{b) }\left(x+y+z-t\right)\left(x+y-z+t\right)\)

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

\(=\left(x+y\right)^2-\left(z-t\right)^2\)

\(=\left(x^2+2xy+y^2\right)-\left(z^2-2zt+t^2\right)\)

\(=x^2+2xy+y^2-z^2+2zt-t^2\)