5 The binomial expansion of \(( 2 + 5 x ) ^ { 4 }\) is given by
$$( 2 + 5 x ) ^ { 4 } = A + 160 x + B x ^ { 2 } + 1000 x ^ { 3 } + 625 x ^ { 4 }$$
5
- Find the value of \(A\) and the value of \(B\).
[0pt]
[2 marks]
L
5 - Show that
$$( 2 + 5 x ) ^ { 4 } - ( 2 - 5 x ) ^ { 4 } = C x + D x ^ { 3 }$$
where \(C\) and \(D\) are constants to be found.
5 - Hence, or otherwise, find
$$\int \left( ( 2 + 5 x ) ^ { 4 } - ( 2 - 5 x ) ^ { 4 } \right) \mathrm { d } x$$