Question 7: Simplify the following expressions: \( x\left( {2{x^2} – 3} \right) – {x^2}\left( {5x + 1} \right) + {x^ 2}\)

We have:

\(\begin{array}{l} x\left( {2{x^2} – 3} \right) – {x^2}\left( {5x + 1} \right) + {x^2} = x.2{x^2} – 3x – {x^2}.5x – {x^2}.1 + {x^2} = 2{x^3} – 3x – 5{x^3} – {x^2} + {x^2}\\ = (2{x^3} – 5{x^3}) + ( – {x^2} + {x^2}) – 3x = – 3{ x^3} – 3x \end{array}\)