a) \(5{a^2} - 5ax - 7a + 7x \)
\(= 5a\left( {a - x} \right) - 7\left( {a - x} \right) \)
\(= \left( {a - x} \right)\left( {5a - 7} \right).\)
b) \({a^3} + {a^2}b - {a^2}c - abc \)
\(= \left( {{a^3} + {a^2}b} \right) + \left( { - {a^2}c - abc} \right) \)
\(= {a^2}\left( {a + b} \right) - ac\left( {a + b} \right)\)
\( = \left( {a + b} \right)\left( {{a^2} - ac} \right) = a\left( {a + b} \right)\left( {a - c} \right).\)
c) \({x^2} - \left( {a + b} \right)x + ab \)
\(= {x^2} - ax - bx + ab\)
\( = x\left( {x - a} \right) - b\left( {x - a} \right) = \left( {x - a} \right)\left( {x - b} \right).\)
d) \({a^3} + {b^3} + {a^2}c + {b^2}c - abc\)
\(= \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right) + c\left( {{a^2} + {b^2} - ab} \right)\)
\( = \left( {{a^2} - ab + {b^2}} \right)\left( {a + b + c} \right).\)
