Đáp án:
F=-1
Giải thích các bước giải:
\(\begin{array}{l}
A = 3{x^2} - 6xy + 3{y^2} - 2{x^2} - 4xy - 2{y^2} - {x^2} + {y^2}\\
= - 10xy + 2{y^2}\\
B = {\left( {x - 1} \right)^2} - 2\left( {x - 1} \right)\left( {x - 3} \right) + {\left( {x - 3} \right)^2}\\
= {\left( {x - 1 - x + 3} \right)^2} = {2^2} = 4\\
C = {\left( {2x + 3} \right)^2} + 2\left( {2x + 3} \right)\left( {x - 3} \right) + {\left( {x - 3} \right)^2}\\
= {\left( {2x + 3 + x - 3} \right)^2}\\
= 9{x^2}\\
D = \left( {x - 1 + x + 1} \right)\left( {{x^2} - 2x + 1 - \left( {x - 1} \right)\left( {x + 1} \right) + {x^2} + 2x + 1} \right)\\
= 2x\left( {2{x^2} + 2 - {x^2} + 1} \right)\\
= 2x.\left( {{x^2} + 3} \right)\\
= 2{x^3} + 6x\\
E = {x^3} + 8 - \left( {{x^3} - 6{x^2} + 12x - 8} \right) - 6\left( {{x^2} - 1} \right)\\
= {x^3} + 8 - {x^3} + 6{x^2} - 12x + 8 - 6{x^2} + 6\\
= - 12x + 22\\
F = {x^3} - 6{x^2} + 12x - 8 - \left( {{x^3} - 1} \right) + 6\left( {{x^2} - 2x + 1} \right)\\
= {x^3} - 6{x^2} + 12x - 8 - {x^3} + 1 + 6{x^2} - 12x + 6\\
= - 1
\end{array}\)
