Phân tích thành nhân tử
x^2 – 9x – 9y – y^2
y^2 – 8y – 3x^2 + 16
4x^2 + 8y – y^2 – 16
2x^2 – 5x – 7
(x^2 – 2)^2 + 32
2x^2 – 4x – 6
3x^2 – 7x + 2
Phân tích thành nhân tử x^2 – 9x – 9y – y^2 y^2 – 8y – 3x^2 + 16 4x^2 + 8y – y^2 – 16 2x^2 – 5x – 7 (x^2 – 2)^2 + 32 2x^2 – 4x – 6 3x^2 – 7x + 2
By Harper
Giải thích các bước giải:
\[\begin{array}{l}
{x^2} – 9x – 9y – {y^2} = \left( {{x^2} – {y^2}} \right) – \left( {9x + 9y} \right) = \left( {x – y} \right)\left( {x + y} \right) – 9\left( {x + y} \right) = \left( {x + y} \right)\left( {x – y – 9} \right)\\
{y^2} – 8y – 3{x^2} + 16 = \left( {{y^2} – 8y + 16} \right) – 3{x^2} = {\left( {y – 4} \right)^2} – 3{x^2} = \left( {y – 4 – \sqrt 3 x} \right)\left( {y – 4 + \sqrt 3 x} \right)\\
4{x^2} + 8y – {y^2} – 16 = \left( {2{x^2}} \right) – \left( {{y^2} – 8y + 16} \right) = {\left( {2x} \right)^2} – {\left( {y – 4} \right)^2} = \left( {2x – y + 4} \right)\left( {2x + y – 4} \right)\\
2{x^2} – 5x – 7 = 2{x^2} + 2x – 7x – 7 = 2x\left( {x + 1} \right) – 7\left( {x + 1} \right) = \left( {x + 1} \right)\left( {2x – 7} \right)
\end{array}\]