Trang chủ » Hỏi đáp » Môn Toán 2x ( x^2 – 3x + 5 ) – 2x^3 ( x + 2 )^2 – 4x 2x – 6x^2 4x^2 – 12x + 9 x^2 – y^2 – 3x + 3y 15/01/2025 2x ( x^2 – 3x + 5 ) – 2x^3 ( x + 2 )^2 – 4x 2x – 6x^2 4x^2 – 12x + 9 x^2 – y^2 – 3x + 3y
Giải đáp: $\begin{array}{l}a) – 2x\left( {3x – 5} \right)\\b){x^2} + 4\\c)2x.\left( {1 – 3x} \right)\\d){\left( {2x – 3} \right)^2}\\e)\left( {x – y} \right)\left( {x + y – 3} \right)\end{array}$ Lời giải và giải thích chi tiết: $\begin{array}{l}a)2x\left( {{x^2} – 3x + 5} \right) – 2{x^3}\\ = 2{x^3} – 6{x^2} + 10x – 2{x^3}\\ = – 6{x^2} + 10x\\b){\left( {x + 2} \right)^2} – 4x\\ = {x^2} + 4x + 4 – 4x\\ = {x^2} + 4\\c)2x – 6{x^2} = 2x.\left( {1 – 3x} \right)\\d)4{x^2} – 12x + 9\\ = {\left( {2x} \right)^2} – 2.2x.3 + {3^2}\\ = {\left( {2x – 3} \right)^2}\\e){x^2} – {y^2} – 3x + 3y\\ = \left( {x – y} \right)\left( {x + y} \right) – 3.\left( {x – y} \right)\\ = \left( {x – y} \right)\left( {x + y – 3} \right)\end{array}$ Trả lời
a) – 2x\left( {3x – 5} \right)\\
b){x^2} + 4\\
c)2x.\left( {1 – 3x} \right)\\
d){\left( {2x – 3} \right)^2}\\
e)\left( {x – y} \right)\left( {x + y – 3} \right)
\end{array}$
a)2x\left( {{x^2} – 3x + 5} \right) – 2{x^3}\\
= 2{x^3} – 6{x^2} + 10x – 2{x^3}\\
= – 6{x^2} + 10x\\
b){\left( {x + 2} \right)^2} – 4x\\
= {x^2} + 4x + 4 – 4x\\
= {x^2} + 4\\
c)2x – 6{x^2} = 2x.\left( {1 – 3x} \right)\\
d)4{x^2} – 12x + 9\\
= {\left( {2x} \right)^2} – 2.2x.3 + {3^2}\\
= {\left( {2x – 3} \right)^2}\\
e){x^2} – {y^2} – 3x + 3y\\
= \left( {x – y} \right)\left( {x + y} \right) – 3.\left( {x – y} \right)\\
= \left( {x – y} \right)\left( {x + y – 3} \right)
\end{array}$