Toán phân tích thành nhân tử a) 2x^2-12x+18+2xy-6y b) x^2+4x-4y^2+8y 14/09/2021 By Maya phân tích thành nhân tử a) 2x^2-12x+18+2xy-6y b) x^2+4x-4y^2+8y
\(\begin{array}{l} a)\,\,2{x^2} – 12x + 18 + 2xy – 6y\\ = 2\left( {{x^2} – 6x + 9} \right) + 2y\left( {x – 3} \right)\\ = 2{\left( {x – 3} \right)^2} + 2y\left( {x – 3} \right)\\ = 2\left( {x – 3} \right)\left( {x – 3 + 2y} \right).\\ b)\,\,{x^2} + 4x – 4{y^2} + 8y\\ = \left( {{x^2} – 4{y^2}} \right) + \left( {4x + 8y} \right)\\ = \left( {x – 2y} \right)\left( {x + 2y} \right) + 4\left( {x + 2y} \right)\\ = \left( {x + 2y} \right)\left( {x – 2y + 4} \right). \end{array}\) Trả lời
\(\begin{array}{l}
a)\,\,2{x^2} – 12x + 18 + 2xy – 6y\\
= 2\left( {{x^2} – 6x + 9} \right) + 2y\left( {x – 3} \right)\\
= 2{\left( {x – 3} \right)^2} + 2y\left( {x – 3} \right)\\
= 2\left( {x – 3} \right)\left( {x – 3 + 2y} \right).\\
b)\,\,{x^2} + 4x – 4{y^2} + 8y\\
= \left( {{x^2} – 4{y^2}} \right) + \left( {4x + 8y} \right)\\
= \left( {x – 2y} \right)\left( {x + 2y} \right) + 4\left( {x + 2y} \right)\\
= \left( {x + 2y} \right)\left( {x – 2y + 4} \right).
\end{array}\)