\(B3\\ a,x^2-x-y^2-y=\left(x^2-y^2\right)-\left(x+y\right)\\ =\left(x-y\right)\left(x+y\right)-\left(x+y\right) =\left(x+y\right)\left(x-y-1\right)\\ ---\\ b,x^2-2xy+y^2-z^2\\ =\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\\ ---\\ c,x^2-3x+xy-3y\\ =x\left(x-3\right)+y\left(x-3\right)=\left(x+y\right)\left(x-3\right)\\ ---\\ d,2xy+3z+6y+xz=\left(2xy+xz\right)+\left(3z+6y\right)\\ =x\left(2y+z\right)+3\left(z+2y\right)=\left(z+2y\right)\left(x+3\right)\)
Bài 3:
a: \(x^2-x-y^2-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
b: \(x^2-2xy+y^2-z^2\)
\(=\left(x^2-2xy+y^2\right)-z^2\)
\(=\left(x-y\right)^2-z^2\)
\(=\left(x-y-z\right)\left(x-y+z\right)\)
c: \(x^2-3x+xy-3y\)
\(=\left(x^2-3x\right)+\left(xy-3y\right)\)
\(=x\left(x-3\right)+y\left(x-3\right)\)
\(=\left(x-3\right)\left(x+y\right)\)
d: \(2xy+3z+6y+xz\)
\(=\left(xz+2xy\right)+\left(3z+6y\right)\)
\(=x\left(z+2y\right)+3\left(z+2y\right)\)
\(=\left(z+2y\right)\left(x+3\right)\)
Bài 2:
a: \(\left(x+y\right)^2-6\left(x+y\right)+9\)
\(=\left(x+y\right)^2-2\cdot\left(x+y\right)\cdot3+3^2\)
\(=\left(x+y-3\right)^2\)
b: \(16a^2-49\left(b-c\right)^2\)
\(=\left(4a\right)^2-\left(7b-7c\right)^2\)
\(=\left(4a-7b+7c\right)\left(4a+7b-7c\right)\)
c: \(49\left(y-4\right)^2-9\left(y-2\right)^2\)
\(=\left[7\left(y-4\right)\right]^2-\left[3\left(y-2\right)\right]^2\)
\(=\left(7y-28\right)^2-\left(3y-6\right)^2\)
\(=\left(7y-28-3y+6\right)\left(7y-28+3y-6\right)\)
\(=\left(4y-22\right)\left(10y-34\right)\)
\(=4\left(2y-11\right)\left(5y-17\right)\)
