[tex]a) - {x}^{2} + x + {x}^{2} + {x}^{3} + x = \\ ( - {x}^{2} + {x}^{2} ) + (x + x) + {x}^{3} = \\ 2x + {x}^{3} = \\ x(2 + {x}^{2} )[/tex]
[tex]b)8x {y}^{2} - 5 {x}^{2} y + {x}^{2} y - x {y}^{2} = \\ (8x{y}^{2} - x {y}^{2} ) + ( - 5 {x}^{2}y + {x}^{2} y ) = \\ 7x {y}^{2} + ( - 4 {x}^{2} y) = \\ 7x {y}^{2} - 4 {x}^{2} y = \\ xy(7y - 4x)[/tex]
[tex]c)8 {x}^{2} - x + 9x + {x}^{2} = \\ (8 {x}^{2} + {x}^{2} ) + ( - x + 9x) = \\ 9 {x}^{2} + 8x = \\ x(9x + 8)[/tex]
[tex]d)2 {x}^{2} \times 4 {x}^{3} \times 5 {x}^{6} = \\ 2 \times 4 \times 5 \times {x}^{2 + 3 + 6} = \\ 40 {x}^{11} [/tex]
[tex]e) - 3 {x}^{2} \times xyz \times 6 {y}^{3} \times {x}^{2} = \\ (- 3 \times6 ) \times {x}^{2 + 1 + 2} \times {y}^{1 + 3} \times z = \\ - 18 {x}^{5} {y}^{4} z[/tex]
[tex]f)15 {x}^{3} \div5 {x}^{2} = \\ (15 \div 5) \times {x}^{3 - 2} = \\ 3x[/tex]
[tex]g) - 8 {x}^{3} {y}^{2} \div 2 {x}^{2} y = \\ ( - 8 \div 2) \times {x}^{3 - 2} \times {y}^{2 - 1} = \\ - 4xy[/tex]
[tex]h)10 {x}^{4} y {z}^{2} \div 5xyz = \\ (10 \div 5) \times {x}^{4 - 1} \times {y}^{1 -1 } \times {z}^{2 - 1} = \\ 2 {x}^{3} z[/tex]
