a,\(3xy+6x^2=3x\left(y+2x\right)\)
b,\(-4xy^2+8x^2y=-4xy\left(y-2x\right)\)
c,\(4\left(x+y\right)+x^2+xy=4\left(x+y\right)+x\left(x+y\right)\)\(=\left(4+x\right)\left(x+y\right)\)
d,\(4x^2-9y^2=\left(2x\right)^2-\left(3y\right)^2=\left(2x-3y\right)\left(2x+3y\right)\)
e,\(25x^2-\dfrac{1}{4}=\left(5x\right)^2-\left(\dfrac{1}{2}\right)^2=\left(5x-\dfrac{1}{2}\right)\left(5x+\dfrac{1}{2}\right)\)
a. \(=3x\left(y+2x\right)\)
b. \(=4xy\left(-y+2x\right)\)
c. \(=4\left(x+y\right)+x\left(x+y\right)=\left(4+x\right)\left(x+y\right)\)
d. \(=\left(2x+3y\right)\left(2x-3y\right)\)
e. \(=\left(5x+\dfrac{1}{2}\right)\left(5x-\dfrac{1}{2}\right)\)
f. \(=\left(4x+4+3x-6\right)\left(4x+4-3x+6\right)=\left(7x-2\right)\left(x+10\right)\)
g . \(=x^2+x+9x+9=x\left(x+1\right)+9\left(x+1\right)=\left(x+9\right)\left(x+1\right)\)