Polynomial Expansion and Simplification

1 Expand \(( 2 x + 5 ) ( x - 1 ) ( x + 3 )\), simplifying your answer.

2

1. Simplify \(( 3 x + 1 ) ^ { 2 } - 2 ( 2 x - 3 ) ^ { 2 }\).
2. Find the coefficient of \(x ^ { 3 }\) in the expansion of $$\left( 2 x ^ { 3 } - 3 x ^ { 2 } + 4 x - 3 \right) \left( x ^ { 2 } - 2 x + 1 \right)$$

1 Simplify \(( 3 x - 1 ) \left( 2 x ^ { 2 } - 5 x + 3 \right)\).

9 Expand and simplify \(( n + 2 ) ^ { 3 } - n ^ { 3 }\).

5

1. Expand and simplify \(( 2 x + 1 ) ( x - 3 ) ( x + 4 )\).
2. Find the coefficient of \(x ^ { 4 }\) in the expansion of $$x \left( x ^ { 2 } + 2 x + 3 \right) \left( x ^ { 2 } + 7 x - 2 \right) .$$

1 Simplify \(( x - 5 ) \left( x ^ { 2 } + 3 \right) - ( x + 4 ) ( x - 1 )\).

3 Simplify \(\frac { \left( 3 x y ^ { 4 } \right) ^ { 3 } } { 6 x ^ { 5 } y ^ { 2 } }\).

3 Expand and simplify \(( n + 2 ) ^ { 3 } - n ^ { 3 }\).

6 Expand \(( 2 x + 5 ) ( x - 1 ) ( x + 3 )\), simplifying your answer.

1 Find the coefficient of \(x\) in the expansion of $$\left( 4 x ^ { 3 } - 5 x ^ { 2 } + 3 x - 2 \right) \left( x ^ { 5 } + 4 x + 1 \right)$$ Circle your answer.
[0pt] [1 mark] \(\begin{array} { l l l l } - 5 & - 2 & 7 & 11 \end{array}\)