Đáp án:

$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 1:\\ a.\ A=-10x^{2} +4xy\\ b.\ B=24x^{4} -48x^{2} +32x\\ c.\ C=2x^{5} +10x^{4} -x^{3}\\ d.\ D=x^{3} y^{2} z+3xy^{2} z^{2} +4x^{2} y^{3} z^{2}\\ Bài\ 2:\\ a.\ 18x^{4} y^{4} -3x^{3} y^{3} +\frac{6}{5} x^{2} y^{4}\\ b.\ -2x^{4} y+\frac{5}{2} x^{2} y^{2} -x^{2} y\\ c.\ -6x^{8} y^{2} +x^{6} y^{5} +x^{5} y^{7}\\ d.\ 2x^{2} y^{3} +6x^{3} y^{3} -2x^{2} y^{5}\\ Bài\ 3\\ a.\ 5;\ b.\ 16\\ Bài\ 4:\\ a.\ x=2;\ b.\ x=5 \end{array}$

Giải thích các bước giải:

$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 1:\\ a.\ A=-\frac{2}{3} x( 15x-6y) =\frac{-2x.15x}{3} +\frac{2}{3} x.6y=-10x^{2} +4xy\\ b.\ B=8x\left( 3x^{3} -6x+4\right) =24x^{4} -48x^{2} +32x\\ c.\ C=2x^{3} .\left( x^{2} +5x-\frac{1}{2}\right) =2x^{5} +10x^{4} -x^{3}\\ d.\ D=xyz\left( x^{2} y+3yz^{2} +4xy^{2} z\right) =x^{3} y^{2} z+3xy^{2} z^{2} +4x^{2} y^{3} z^{2}\\ Bài\ 2:\\ a.\ \left( 3x^{3} y-\frac{1}{2} x^{2} +\frac{1}{5} xy\right) .6xy^{3} =18x^{4} y^{4} -3x^{3} y^{3} +\frac{6}{5} x^{2} y^{4}\\ b.\ \left( 4x^{3} -5xy+2x\right) .\left( -\frac{1}{2} xy\right) =-2x^{4} y+\frac{5}{2} x^{2} y^{2} -x^{2} y\\ c.\ -x^{4} y^{2}\left( 6x^{4} -x^{2} y^{3} -y^{5}\right) =-6x^{8} y^{2} +x^{6} y^{5} +x^{5} y^{7}\\ d.\ 2xy^{2}\left( xy+3x^{2} y-xy^{3}\right) =2x^{2} y^{3} +6x^{3} y^{3} -2x^{2} y^{5}\\ Bài\ 3:\\ a.\ A=x( 2x+1) -x^{2}( x+2) +\left( x^{3} -x+5\right)\\ =2x^{2} +x-x^{3} -2x^{2} +x^{3} -x+5=5\Leftrightarrow đpcm\\ b.\ B=x\left( 3x^{2} -x+5\right) -\left( 2x^{3} +3x-16\right) -x\left( x^{2} -x+2\right)\\ =3x^{3} -x^{2} +5x-2x^{3} -3x+16-x^{3} +x^{2} -2x=16\Leftrightarrow đpcm\\ Bài\ 4:\\ a.\ 3x( 12x-4) -9x( 4x-3) =30\\ \Leftrightarrow 36x^{2} -12x-36x^{2} +27x=30\\ \Leftrightarrow 15x=30\Leftrightarrow x=2\\ b.\ x( 5-2x) +2x( x-1) =15\\ \Leftrightarrow 5x-2x^{2} +2x^{2} -2x=15\\ \Leftrightarrow 3x=15\Leftrightarrow x=5 \end{array}$