Đáp án:
$1.5x^5-x^3-\dfrac{1}{2}x^2\\
2.2x^3y^2-\dfrac{2}{3}x^4y+\dfrac{2}{3}x^2y^2\\
3.-2x^4y+\dfrac{5}{2}x^2y^2-x^2y\\
4.
2x^3+6x^3+x^2\\
6.
-x^3y^3+\dfrac{1}{2}x^3y^2-\dfrac{3}{4}x^4y^3\\
7.
x^3y^2z+3xy^2z^3+4x^2y^3z^2\\
10.
6x^4-x^3-12x^2\
8. x^3y^3+x^4y^4+3x^3y^5\\
9.
\dfrac{2}{3}x^4+\dfrac{2}{3}x^5-\dfrac{1}{2}x^8\\
5.
2x^2y^3+6x^3y^3-\dfrac{4}{3}x^2y^5$
Giải thích các bước giải:
$1.x^2(5x^3-x-\dfrac{1}{2})\\
=5x^5-x^3-\dfrac{1}{2}x^2\\
2.(3xy-x^2+y).\dfrac{2}{3}x^2y\\
=3xy.\dfrac{2}{3}x^2-x^2.\dfrac{2}{3}x^2y+y.\dfrac{2}{3}x^2y\\
=2x^3y^2-\dfrac{2}{3}x^4y+\dfrac{2}{3}x^2y^2\\
3.(4x^3-5xy+2x).\left ( -\dfrac{1}{2}xy \right )\\
=4x^3.\left ( -\dfrac{1}{2}xy \right )-5xy.\left ( -\dfrac{1}{2}xy \right )+2x.\left ( -\dfrac{1}{2}xy \right )\\
=-2x^4y+\dfrac{5}{2}x^2y^2-x^2y\\
4.
2x^2(x^2+3x+\dfrac{1}{2})\\
=2x^3+6x^3+x^2\\
6.
-x^2y(xy^2-\dfrac{1}{2}xy+\dfrac{3}{4}x^2y^2)\\
=-x^3y^3+\dfrac{1}{2}x^3y^2-\dfrac{3}{4}x^4y^3\\
7.
xyz(x^2y+3yz^2+4xy^2z)\\
=x^3y^2z+3xy^2z^3+4x^2y^3z^2\\
10.
3x.(2x^3-\dfrac{1}{3}x^2-4x)\\
=6x^4-x^3-12x^2\
8. xy^2(x^2y+x^3y^2+3x^2y^3)\\
=x^3y^3+x^4y^4+3x^3y^5\\
9.
\dfrac{2}{3}x^3.(x+x^2-\dfrac{3}{4}x^5)\\
=\dfrac{2}{3}x^4+\dfrac{2}{3}x^5-\dfrac{1}{2}x^8\\
5.
2xy^2(xy+3x^2y-\dfrac{2}{3}xy^3)\\
=2x^2y^3+6x^3y^3-\dfrac{4}{3}x^2y^5$
