Đáp án:
$a. x^{2} + 6x + 9 = ( x^{2} + 3x ) + ( 3x + 9 )$
⇔ $x^{2} + 6x + 9 = x( x + 3 ) + 3( x + 3 )$
⇔ $x^{2} + 6x + 9 = ( x + 3 )^{2}$
$b. x^{2} + x + \frac{1}{4} = ( x^{2} + \frac{1}{2}x ) + ( \frac{1}{2}x + \frac{1}{4} )$
⇔ $x^{2} + x + \frac{1}{4} = x( x + \frac{1}{2} ) + \frac{1}{2}( x + \frac{1}{2} )$
⇔ $x^{2} + x + \frac{1}{4} = ( x + \frac{1}{2} )^{2}$
$c. 2xy^{2} + x^{2}y^{4} + 1 = ( x^{2}y^{4} + xy^{2} ) + ( xy^{2} + 1 )$
⇔ $2xy^{2} + x^{2}y^{4} + 1 = xy^{2}( xy^{2} + 1 ) + ( xy^{2} + 1 )$
⇔ $2xy^{2} + x^{2}y^{4} + 1 = ( xy^{2} + 1 )^{2}$
