Bài 1:
a) Ta có: \(\left(x+2\right)\left(3x+1\right)\)
\(=3x^2+x+6x+2\)
\(=3x^2+7x+2\)
b) Ta có: \(\left(5x+2\right)\left(x-3\right)\)
\(=5x^2-15x+2x-6\)
\(=5x^2-13x-6\)
c) Ta có: \(\left(2x-3\right)\left(2x+3\right)\)
\(=4x^2+6x-6x-9\)
\(=4x^2-9\)
d) Ta có: (2x-1)(3x-2)
\(=6x^2-4x-3x+2\)
\(=6x^2-7x+2\)
e) Ta có: \(\left(2x+5\right)\left(x-3\right)-2x^2+x\)
\(=2x^2-6x+5x-15-2x^2+x\)
=-15
f) Ta có: \(\left(2x+1\right)\left(3x-2\right)-6x^2\)
\(=6x^2-4x+3x-2-6x^2\)
\(=-x-2\)
g) Ta có: \(\left(2x-1\right)\left(2x-1\right)\left(2x-1\right)\)
\(=\left(2x-1\right)^3\)
\(=8x^2-12x^2+6x-1\)
h) Ta có: \(\left(x+y-z\right)\left(x+y+z\right)\)
\(=\left(x+y\right)^2-z^2\)
\(=x^2+2xy+y^2-z^2\)
Bài 2:
a) Ta có: \(3x\left(2-3x\right)+\left(x+2\right)\left(9x-4\right)\)
\(=6x-9x^2+9x^2-4x+18x-8\)
\(=5x-8\)
b) Ta có: \(x\left(x-3\right)+\left(x-1\right)\left(x+5\right)\)
\(=x^2-3x+x^2+5x-x-5\)
\(=2x^2+x-5\)
c) Ta có: \(\left(x-1\right)\left(x+3\right)-\left(x-2\right)\left(x+2\right)\)
\(=x^2+3x-x-3-x^2+4\)
\(=2x+1\)
d) Ta có: \(\left(2x-3\right)\left(2x+3\right)-4x\left(x+7\right)\)
\(=4x^2-9-4x^2-28x\)
\(=-28x-9\)
e) Ta có: \(\left(x-1\right)\left(x^2+x+1\right)-x\left(x^2+2\right)\)
\(=x^3-1-x^3-2x\)
=-2x-1
