Question

bài 1:rút gọn biểu thức

a,(2x-5y)(3x-4y)-(x-y)(6x-21y)

b,(x-y)²-(x+y)²

c, (x-1)(x²+3x+1)-x(x²-2)

Answer 1

Bài 1: Rút gọn biểu thức

a) Ta có: (2x-5y)(3x-4y)-(x-y)(6x-21y)

\(=6x^2-8xy-15xy+20y^2-\left(6x^2-21xy-6xy+21y^2\right)\)

\(=6x^2-23xy+20y^2-6x^2+27xy-21y^2\)

\(=4xy-y^2\)

b) Ta có: \(\left(x-y\right)^2-\left(x+y\right)^2\)

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

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

\(=-2y\cdot2x=-4xy\)

c) Ta có: \(\left(x-1\right)\left(x^2+3x+1\right)-x\left(x^2-2\right)\)

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

\(=2x^2-1\)