Đáp án:
e) \(\left( {x + 2y} \right)\left( {x - 2y - 2} \right)\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left( {x + 1} \right)\left( {x + 3} \right) - x\left( {x + 2} \right) = 7\\
\to {x^2} + 4x + 3 - {x^2} - 2x = 7\\
\to 2x = 4\\
\to x = 2\\
b)2x + 2y - {x^2} - xy\\
= 2\left( {x + y} \right) - x\left( {x + y} \right)\\
= \left( {x + y} \right)\left( {2 - x} \right)\\
c){x^2} - 25 + {y^2} + 2xy\\
= \left( {{x^2} + 2xy + {y^2}} \right) - 25\\
= {\left( {x + y} \right)^2} - 25\\
= \left( {x + y - 5} \right)\left( {x + y + 5} \right)\\
d){a^2} + 2ab + {b^2} - ac - bc\\
= {\left( {a + b} \right)^2} - c\left( {a + b} \right)\\
= \left( {a + b} \right)\left( {a + b - c} \right)\\
e){x^2} - 2x - 4{y^2} - 4y\\
= {x^2} - 4{y^2} - 2\left( {x + 2y} \right)\\
= \left( {x - 2y} \right)\left( {x + 2y} \right) - 2\left( {x + 2y} \right)\\
= \left( {x + 2y} \right)\left( {x - 2y - 2} \right)
\end{array}\)
