\(a)\)\( P = \left( {5x - 1} \right) + 2\left( {1 - 5x} \right)\left( {4 + 5x} \right) \)\(+ {\left( {5x + 4} \right)^2}\)
\( = 5x - 1 + 8 + 10x - 40x - 50{x^2} \)\(+ 25{x^2} + 40x + 16 \)
\(=\left( { - 50{x^2} + 25{x^2}} \right)\)\( + \left( {5x + 10x - 40x + 40x} \right)\)\( + \left( { - 1 + 8 + 16} \right) \)
\(= - 25{x^2} + 15x + 23 \)
\(b)\) \(Q = {\left( {x - y} \right)^3} + {\left( {y + x} \right)^3} + {\left( {y - x} \right)^3}\)\( - 3xy\left( {x + y} \right)\)
\( = {x^3} - 3{x^2}y + 3x{y^2} - {y^3} + {y^3} + 3x{y^2}\)\( + 3{x^2}y + {x^3} + {y^3} - 3x{y^2} + 3{x^2}y - {x^3} \)\(- 3{x^2}y - 3x{y^2} = {x^3} + {y^3} \)
