a) \( 14 a^{3} b^{5}+35 a^{2} b^{2}+49 a^{2} b+7 a^{2} b \)

First, let’s simplify the expression by combining like terms: \[ 14 a^{3} b^{5} + (35 a^{2} b^{2} + 49 a^{2} b + 7 a^{2} b) \] The like terms for \( a^{2} b \) sum up to \( 49 a^{2} b + 7 a^{2} b = 56 a^{2} b \). So, the expression becomes: \[ 14 a^{3} b^{5} + 35 a^{2} b^{2} + 56 a^{2} b \] Now, we can factor out common terms: - The first term has the coefficient 14, and we can factor out \( 7a^{2} \) from the last two terms: \[ = 14 a^{3} b^{5} + 7 a^{2} (5 b^{2} + 8 b) \] So, the fully simplified expression is: \[ 14 a^{3} b^{5} + 7 a^{2} (5 b^{2} + 8 b) \] This is your completed polynomial!