Generalised Binomial Theorem and Partial Fractions
8
Express \(\frac { 7 x ^ { 2 } + 8 } { ( 1 + x ) ^ { 2 } ( 2 - 3 x ) }\) in partial fractions.
Hence expand \(\frac { 7 x ^ { 2 } + 8 } { ( 1 + x ) ^ { 2 } ( 2 - 3 x ) }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 2 }\), simplifying the coefficients.