Đáp án:
$\begin{array}{l}
B1)a)12{a^2}b\left( {a - b} \right)\left( {a + b} \right)\\
= 12{a^2}b\left( {{a^2} - {b^2}} \right)\\
= 12{a^4}b - 12{a^2}{b^3}\\
b)\left( {2{x^2} - 3x + 5} \right)\left( {{x^2} - 8x + 2} \right)\\
= 2{x^4} - 16{x^3} + 4{x^2} - 3{x^3} + 24{x^2} - 6x\\
+ 5{x^2} - 40x + 10\\
= 2{x^4} - 19{x^3} + 33{x^2} - 46x + 10\\
B2)\\
a)\dfrac{1}{4}{x^2} - \left( {\dfrac{1}{2}x - 4} \right).\dfrac{1}{2}x = - 14\\
\Leftrightarrow \dfrac{1}{4}{x^2} - \dfrac{1}{4}{x^2} + 2x = - 14\\
\Leftrightarrow 2x = - 14\\
\Leftrightarrow x = - 7\\
Vay\,x = - 7\\
b)3\left( {1 - 4x} \right)\left( {x - 1} \right) + 4\left( {3x - 2} \right)\left( {x + 3} \right) = - 27\\
\Leftrightarrow 3\left( { - 4{x^2} + 5x - 1} \right) + 4\left( {3{x^2} + 7x - 6} \right) = - 27\\
\Leftrightarrow - 12{x^2} + 15x - 3 + 12{x^2} + 28x - 24 = - 27\\
\Leftrightarrow 43x = 0\\
\Leftrightarrow x = 0\\
Vay\,x = 0\\
B3)\\
1)A = 5x\left( {4{x^2} - 2x + 1} \right) - 2x\left( {10{x^2} - 5x - 2} \right)\\
= 20{x^3} - 10{x^2} + 5x - 20{x^3} + 10{x^2} + 4x
\end{array}$
$\begin{array}{l}
A = 9x\\
= 9.15 = 135\left( {do:x = 15} \right)\\
2)B = 5x\left( {x - 4y} \right) - 4y\left( {y - 5x} \right)\\
= 5{x^2} - 20xy - 4{y^2} + 20xy\\
= 5{x^2} - 4{y^2}\\
= 5.{\left( {\dfrac{{ - 1}}{5}} \right)^2} - 4.{\left( {\dfrac{{ - 1}}{2}} \right)^2}\\
= \dfrac{1}{5} - 1\\
= - \dfrac{4}{5}\\
3)C = 6xy\left( {xy - {y^2}} \right) - 8{x^2}\left( {x - {y^2}} \right)\\
+ 5{y^2}\left( {{x^2} - xy} \right)\\
= 6{x^2}{y^2} - 6x{y^3} - 8{x^3} + 8{x^2}{y^2}\\
+ 5{x^2}{y^2} - 5x{y^3}\\
= 19{x^2}{y^2} - 11x{y^3} - 8{x^3}\\
= 19.{\left( {\dfrac{1}{2}} \right)^2}{.2^2} - 11.\dfrac{1}{2}{.2^3} - 8.\dfrac{1}{{{2^3}}}\\
= 19 - 11.4 - 1\\
= - 26\\
4)D = \left( {{y^2} + 2} \right)\left( {y - 4} \right) - \left( {2{y^2} + 1} \right)\left( {\dfrac{1}{2}y - 2} \right)\\
= {y^3} - 4{y^2} + 2y - 8 - \left( {{y^3} - 4{y^2} + \dfrac{1}{2}y - 2} \right)\\
= \dfrac{3}{2}y - 6\\
= \dfrac{3}{2}.\dfrac{{ - 2}}{3} - 6\\
= - 1 - 6\\
= - 7
\end{array}$
