Thực hiện phép tính:
a)3xy.(2x^2-3yz+x^3)
b)(24x^5-12x^4+6x^2):6x^2
c)(2x+3)^2+(2x-3)^2-(2x+3)(4x-6)+xy
d)(8x^3y-16xy^2+10x^2y^2):(2xy)
e)(x^3-3x^2+3x-1):(x^2-2x+1)
Thực hiện phép tính:
a)3xy.(2x^2-3yz+x^3)
b)(24x^5-12x^4+6x^2):6x^2
c)(2x+3)^2+(2x-3)^2-(2x+3)(4x-6)+xy
d)(8x^3y-16xy^2+10x^2y^2):(2xy)
e)(x^3-3x^2+3x-1):(x^2-2x+1)
Đáp án:
\(\begin{array}{l}
a)\,\,\,6{x^3}y – 9x{y^2}z + 3{x^4}y\\
b)\,\,4{x^3} – 2{x^2} + 1\\
c)\,\,36 + xy\\
d)\,\,4{x^2} – 8y + 5xy\\
e)\,\,x – 1
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\,\,3xy.\left( {2{x^2} – 3yz + {x^3}} \right) = 6{x^3}y – 9x{y^2}z + 3{x^4}y.\\
b)\,\,\left( {24{x^5} – 12{x^4} + 6{x^2}} \right):6{x^2} = 6{x^2}\left( {4{x^3} – 2{x^2} + 1} \right):6{x^2} = 4{x^3} – 2{x^2} + 1.\\
c)\,\,{\left( {2x + 3} \right)^2} + {\left( {2x – 3} \right)^2} – \left( {2x + 3} \right)\left( {4x – 6} \right) + xy\\
= \,{\left( {2x + 3} \right)^2} + {\left( {2x – 3} \right)^2} – 2\left( {2x + 3} \right)\left( {2x – 3} \right) + xy\\
= {\left( {2x + 3 – 2x + 3} \right)^2} + xy = 36 + xy.\\
d)\,\left( {\,8{x^3}y – 16x{y^2} + 10{x^2}{y^2}} \right):\left( {2xy} \right)\\
= 2xy\left( {4{x^2} – 8y + 5xy} \right):\left( {2xy} \right)\\
= 4{x^2} – 8y + 5xy.\\
e)\,\,\left( {{x^3} – 3{x^2} + 3x – 1} \right):\left( {{x^2} – 2x + 1} \right)\\
= {\left( {x – 1} \right)^3}:{\left( {x – 1} \right)^2}\\
= x – 1.
\end{array}\)