Fully simplify \( 6 x^{2} y+3 y x+4 x y+3 x y^{2}+2 y x^{2} \)

To fully simplify the expression \( 6 x^{2} y + 3 y x + 4 x y + 3 x y^{2} + 2 y x^{2} \), we start by rearranging and grouping like terms. First, let's rewrite it: - \( 6 x^2 y + 2 x^2 y + 3 y x + 4 x y + 3 x y^2 \) Now combine the like terms: - The \( x^2 y \) terms: \( 6 x^2 y + 2 x^2 y = (6 + 2)x^2 y = 8 x^2 y \) - The \( xy \) terms: \( 3 y x + 4 x y = (3 + 4)xy = 7xy \) So now we have: - \( 8 x^2 y + 7 x y + 3 x y^2 \) Now, let's keep all this in mind: - We can look for a common factor in the terms \( 8 x^2 y, 7xy, \) and \( 3xy^2 \). All these terms have \( xy \) in common. Factoring out \( xy \) gives us: - \( xy(8x + 7 + 3y) \) Thus, the fully simplified expression is: \[ xy(8x + 7 + 3y) \]