Đáp án:

 $a)\dfrac{1}{2}x^4y^2-\dfrac{1}{4}x^5y^2+\dfrac{1}{2}x^2y\\
b)
\dfrac{-1}{3}x^3y^2-2x^2y^3+\dfrac{1}{3}xy\\
c)
-x^3y^2-x^2y^2+xy^2\\
d)
x^3-5x^2-x+5\\
e)
2x^2y^2-\dfrac{41}{2}xy+5\\
f)
\dfrac{1}{2}x^4y+x^3y-3x^3y-6x^2y$

Giải thích các bước giải:

 $a) \dfrac{1}{2}x^2y(x^2y-\dfrac{1}{2}x^3y+1)\\
=\dfrac{1}{2}x^2y.x^2y-\dfrac{1}{2}x^2y.\dfrac{1}{2}x^3y+\dfrac{1}{2}x^2y\\
=\dfrac{1}{2}x^4y^2-\dfrac{1}{4}x^5y^2+\dfrac{1}{2}x^2y\\
b)
\dfrac{-1}{3}xy(x^2y+6xy^2-1)\\
=\dfrac{-1}{3}xy.x^2y+\dfrac{-1}{3}xy.6xy^2-\dfrac{-1}{3}xy\\
=\dfrac{-1}{3}x^3y^2-2x^2y^3+\dfrac{1}{3}xy\\
c)
(x^2+x-1)(-xy^2)\\
=x^2.(-xy^2)+x.(-xy^2)-1.(-xy^2)\\
=-x^3y^2-x^2y^2+xy^2\\
d)
(x-1)(x+1)(x-5)\\
=(x^2-1)(x-5)\\
=x^2.(x-5)-(x-5)\\
=x^2x-5x^2-x+5\\
=x^3-5x^2-x+5\\
e)
\left ( \dfrac{1}{2}xy-5 \right )(4xy-1)\\
=\dfrac{1}{2}xy(4xy-1)-5(4xy-1)\\
=\dfrac{1}{2}xy.4xy-\dfrac{1}{2}xy-20xy+5\\
=2x^2y^2-\dfrac{1}{2}xy-20xy+5\\
=2x^2y^2-\dfrac{41}{2}xy+5\\
f)
\dfrac{3}{2}x^2y\left ( \dfrac{1}{3}x-2 \right )(x+2)\\
=\left ( \dfrac{3}{2}x^2y.\dfrac{1}{3}x-\dfrac{3}{2}x^2y.2 \right )(x+2)\\
=\left ( \dfrac{1}{2}x^3y-3 x^2y\right ).(x+2)\\
=\dfrac{1}{2}x^3y.(x+2)-3 x^2y.(x+2)\\
=\dfrac{1}{2}x^4y+x^3y-3x^3y-6x^2y$

Đáp án:

Giải thích các bước giải:

 a)12x2y(x2y−12x3y+1)=12x2y.x2y−12x2y.12x3y+12x2y=12x4y2−14x5y2+12x2yb)−13xy(x2y+6xy2−1)=−13xy.x2y+−13xy.6xy2−−13xy=−13x3y2−2x2y3+13xyc)(x2+x−1)(−xy2)=x2.(−xy2)+x.(−xy2)−1.(−xy2)=−x3y2−x2y2+xy2d)(x−1)(x+1)(x−5)=(x2−1)(x−5)=x2.(x−5)−(x−5)=x2x−5x2−x+5=x3−5x2−x+5e)(12xy−5)(4xy−1)=12xy(4xy−1)−5(4xy−1)=12xy.4xy−12xy−20xy+5=2x2y2−12xy−20xy+5=2x2y2−412xy+5f)32x2y(13x−2)(x+2)=(32x2y.13x−32x2y.2)(x+2)=(12x3y−3x2y).(x+2)=12x3y.(x+2)−3x2y.(x+2)=12x4y+x3y−3x3y−6x2y