Bài 3:
a) Ta có: \(x^2+4xy-21y^2\)
\(=x^2+7xy-3xy-21y^2\)
\(=x\left(x+7y\right)-3y\left(x+7y\right)\)
\(=\left(x+7y\right)\left(x-3y\right)\)
b) Ta có: \(5x^2+6xy+y^2\)
\(=5x^2+5xy+xy+y^2\)
\(=5x\left(x+y\right)+y\left(x+y\right)\)
\(=\left(x+y\right)\left(5x+y\right)\)
c) Ta có: \(x^2+2xy-15y^2\)
\(=x^2+5xy-3xy-15y^2\)
\(=x\left(x+5y\right)-3y\left(x+5y\right)\)
\(=\left(x+5y\right)\left(x-3y\right)\)
d) Ta có: \(\left(x-y\right)^2+4\left(x-y\right)-12\)
\(=\left(x-y\right)^2+6\left(x-y\right)-2\left(x-y\right)-12\)
\(=\left(x-y\right)\left(x-y+6\right)-2\left(x-y+6\right)\)
\(=\left(x-y+6\right)\left(x-y-2\right)\)
e) Ta có: \(x^2-7xy+10y^2\)
\(=x^2-2xy-5xy+10y^2\)
\(=x\left(x-2y\right)-5y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-5y\right)\)
f) Ta có: \(x^2yz+5xyz-14yz\)
\(=yz\left(x^2+5x-14\right)\)
\(=yz\left(x^2+7x-2x-14\right)\)
\(=yz\left[x\left(x+7\right)-2\left(x+7\right)\right]\)
\(=yz\left(x+7\right)\left(x-2\right)\)
