\(\begin{array}{l}a)\,\,{x^2} + 2xy - 15{y^2}\\ = {x^2} - 3xy + 5xy - 15{y^2}\\ = \left( {{x^2} - 3xy} \right) + \left( {5xy - 15{y^2}} \right)\\ = x\left( {x - 3y} \right) + 5y\left( {x - 3y} \right)\\ = \left( {x - 3y} \right)\left( {x + 5y} \right)\end{array}\)
b) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2\)\(\,+3xyz\)
\( = ({x^2}y + {x^2}z + xyz) \)\(\,+ (x{y^2} + {y^2}z + xyz) \)\(\,+ (x{z^2} + y{z^2} + xyz)\)
\( = x\left( {xy + xz + yz} \right) \)\(\,+ y\left( {xy + yz + xz} \right) \)\(\,+ z\left( {xz + yz + xy} \right)\)
\(= \left( {x + y + z} \right)\left( {xy + xz + yz} \right)\).
