a, \(3x^2\left(x+1\right)-2\left(x+1\right)\)\(=\left(x+1\right)\left(3x^3-2\right)\)
b, \(4x^2\left(x-2y\right)-20x\left(2y-x\right)\)
\(=4x^2\left(x-2y\right)-20x\left[-\left(x-2y\right)\right]\)
\(=4x^2\left(x-2y\right)+20x\left(x-2y\right)\)
\(=\left(4x^2+20x\right)\left(x-2y\right)\)
\(=\left(4x^2+20x\right)\left(x-2y\right)\)
\(=4x\left(x+5\right)\left(x-2y\right)\)
c, \(3x^2y^2\left(a-b+c\right)+2xy\left(b-a-c\right)\)
\(=3x^2y^2\left(a-b+c\right)+2xy\left[-\left(a-b+c\right)\right]\)
\(=3x^2y^2\left(a-b+c\right)-2xy\left(a-b+c\right)\)
\(=\left(3x^2y^2-2xy\right)\left(a-b+c\right)\)
\(=xy\left(3xy-2\right)\left(a-b+c\right)\)
d, \(4x^2-4x+1\)\(=\left(2x\right)^2-2.2x.1+1^2\)\(=\left(2x-1\right)^2\)
j, \(16x^2+24xy+9y^2\)
\(=\left(4x\right)^2+2.4x.3y+\left(3y\right)^2\)
\(=\left(4x-3y\right)^2\)
g, \(x^2-64y^2\)\(=x^2-\left(8y\right)^2\)\(=\left(x-8y\right)\left(x+8y\right)\)
