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a. \(\left[ {5{{\left( {a – b} \right)}^3} + 2{{\left( {a – b} \right)}^2}} \right]:{\left( {b – a} \right)^2}\)
b. \(5{\left( {x – 2y} \right)^3}:\left( {5x – 10y} \right)\)
c. \(\left( {{x^3} + 8{y^3}} \right):\left( {x + 2y} \right)\)
a. \(\left[ {5{{\left( {a – b} \right)}^3} + 2{{\left( {a – b} \right)}^2}} \right]:{\left( {b – a} \right)^2}\)
\( = \left[ {5{{\left( {a – b} \right)}^3} + 2{{\left( {a – b} \right)}^2}} \right]:{\left( {a – b} \right)^2} = 5\left( {a – b} \right) + 2\)
b. \(5{\left( {x – 2y} \right)^3}:\left( {5x – 10y} \right))\ $ = 5{\left( {x – 2y} \right)^3}:5\left( {x – 2y} \right) = {\left( {x – 2y} \right)^2}\)
c. \(\left( {{x^3} + 8{y^3}} \right):\left( {x + 2y} \right))\ $ = \left[ {{x^3} + {{\left( {2y} \right)}^3}} \right]:\left( {x + 2y} \right)\)
\( = \left( {x + 2y} \right)\left( {{x^2} – 2xy + 4{y^2}} \right):\left( {x + 2y} \right) = {x^2} – 2xy + 4{y^2}\)