Đáp án:
$1)
a) \dfrac{2}{3}x^2y^3-x^3y^2+\dfrac{5}{3}xy^3\\
b)
\dfrac{1}{3}x^3y^2-2x^2y^3+\dfrac{1}{3}xy^4-x^2y+6xy^2-y^3\\
c)4x-8\\
d) 28\\
2) a) x=\dfrac{16}{37}\\
b) x=\dfrac{-16}{5}$
Giải thích các bước giải:
$1)
a) (2xy-3x^2+5y)\dfrac{1}{3}xy^2\\
=2xy.\dfrac{1}{3}xy^2-3x^2.\dfrac{1}{3}xy^2+5y.\dfrac{1}{3}xy^2\\
=\dfrac{2}{3}x^2y^3-x^3y^2+\dfrac{5}{3}xy^3\\
b)
(x^2-6xy+y^2)\left ( \dfrac{1}{3}xy^2-y \right )\\
=(x^2-6xy+y^2).\dfrac{1}{3}xy^2-(x^2-6xy+y^2).y\\
=\dfrac{1}{3}x^3y^2-2x^2y^3+\dfrac{1}{3}xy^4-x^2y+6xy^2-y^3\\
c) (x-2)(x+2)-(x-2)^2\\
=x^2-4-(x^2-4x+4)\\
=x^2-4-x^2+4x-4\\
=4x-8\\
d) (x+3)(x^2-3x+9)-(x^3-1)\\
=x^3+3^3-x^3+1\\
=28\\
2) a) 8x(x+5)-x(3+8x)=16\\
\Leftrightarrow 8x^2+40x-3x-8x^2=16\\
\Leftrightarrow (8x^2-8x^2)+37x=16\\
\Leftrightarrow 37x=16\\
\Leftrightarrow x=\dfrac{16}{37}\\
b) x(x+5)-(x-4)(x+4)=6\\
\Leftrightarrow x^2+5x-(x^2-16)=6\\
\Leftrightarrow x^2+5x-x^2+16=0\\
\Leftrightarrow 5x=-16\\
\Leftrightarrow x=\dfrac{-16}{5}$
