Thu gọn các biểu thức sau: (a) A=2x(x+1)+(x+2)(1−2x). (b) B=(x+1)^2+(2x−1)(2x+1).

a) \(A = 2x\left( {x + 1} \right) + \left( {x + 2} \right)\left( {1 - 2x} \right)\)

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

\(A = - x + 2\).

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

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

\(B = 5{x^2} + 2x\).

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

\(C = {x^3} + 8 - 2{x^2} - 8\)

\(C = {x^3} - 2{x^2}\).

d) \(D = \left( {2x + 4} \right)\left( {x - 2} \right) + {(x - 2)^2} + {(x + 2)^2}\)

\(D = {(x + 2)^2} + 2\left( {x + 2} \right)\left( {x - 2} \right) + {(x - 2)^2}\)

\(D = {(x + 2 + x - 2)^2}\)

\(D = {(2x)^2}\)

\(D = 4{x^2}\).