Rút gọn các biểu thức sau (a) A=2x(x−y)+2y(x+y)−(x−y)(x+y) (b) B=(x−4)^2+(x+2)^2−2x(x−1)

a) \(A = 2x\left( {x - y} \right) + 2y\left( {x + y} \right) - \left( {x - y} \right)\left( {x + y} \right)\)

\( = 2{x^2} - 2xy + 2xy + 2{y^2} - {x^2} + {y^2}\)

\( = {x^2} + 3{y^2}\)

b) \(B = {\left( {x - 4} \right)^2} + {\left( {x + 2} \right)^2} - 2x\left( {x - 1} \right)\)

\( = {x^2} - 8x + 16 + {x^2} + 4x + 4 - 2{x^2} + 2x\)

\( = - 2x + 20\)

c) \(C = \left( {4 - x} \right)\left( {4 + x} \right) + \left( {3{x^4} - 6{x^3} + 9{x^2}} \right):\left( {3{x^2}} \right)\)

\( = 16 - {x^2} + {x^2} - 2x + 3\)

\( = 19 - 2x\)