Question

x^4 * (1-x) - (1-x)(x^2-x)^2

Answer 1

$x {}^{4} \times (1 - x) - (1 - x)(x {}^{2} - {}^{} x) {}^{2} = x {}^{4} - x {}^{5} - ((1 - x)(x {}^{4} - 2x {}^{3} + x {}^{2} )) = x {}^{4} - x {}^{5} - (x {}^{4} - 2x {}^{3} + x {}^{2} - x {}^{5} + 2x {}^{3} - x {}^{3} ) = x {}^{4} - x {}^{5} - x {}^{4} + 2x {}^{3} - x {}^{2} + x {}^{5} - 2x {}^{3} + x {}^{3} = x {}^{2} + x {}^{3} = x {}^{2} (1 + x)$