a) \({x^2} + 2x + 1 \)
\(= {x^2} + 2.x.1 + {1^2} = {\left( {x + 1} \right)^2}\)
b) \(9{x^2} + {y^2} + 6xy \)
\(= 9{x^2} + 6xy + {y^2} \)\(= {\left( {3x} \right)^2} + 2.3.x.y + {y^2} = {\left( {3x + y} \right)^2}\)
c) \(25{a^2} + 4{b^2}-20ab \)
\(= 25{a^2}-20ab + 4{b^2} \)
\(= {\left( {5a} \right)^2}-2.5a.2b{\rm{ }} + {\left( {2b} \right)^2}\)
\(= {\left( {5a-2b} \right)^2}\)
Hoặc
\(25{a^2} + 4{b^2}-20ab \)
\(= 4{b^2}-20ab + 25{a^2}\)
\(= {\left( {2b} \right)^2}-2.2b.5a + {\left( {5a} \right)^2}\)
\(= {\left( {2b-5a} \right)^2}\)
d) \({x^2} - x + \dfrac{1}{4} \)
\(= {x^2} - 2.x.\dfrac{1}{2} + {\left( {\dfrac{1}{2}} \right)^2} \)
\( = {\left( {x - \dfrac{1}{2}} \right)^2}\)
Hoặc
\({x^2} - x + \dfrac{1}{4} = \dfrac{1}{4} - x + {x^2} \)
\( = {\left( {\dfrac{1}{2}} \right)^2} - 2.\dfrac{1}{2}.x + {x^2} = {\left( {\dfrac{1}{2} - x} \right)^2}\)
