Question

Rút gọn các biểu thức sau:

a)      \({\left( {x - 3y} \right)^2} - {\left( {x + 3y} \right)^2}\) 

b)      \({\left( {3x + 4y} \right)^2} + {\left( {4x - 3y} \right)^2}\)

Answer 1

a)      \({\left( {x - 3y} \right)^2} - {\left( {x + 3y} \right)^2} = \left( {x - 3y + x + 3y} \right).\left( {x - 3y - x - 3y} \right) = \left( {2x} \right).\left( { - 6y} \right) =  - 12xy\)

b)       

\(\begin{array}{l}{\left( {3x + 4y} \right)^2} + {\left( {4x - 3y} \right)^2} = {\left( {3x} \right)^2} + 2.3x.4y + {\left( {4y} \right)^2} + {\left( {4x} \right)^2} - 2.4x.3y + {\left( {3y} \right)^2}\\ = 9{x^2} + 24xy + 16{y^2} + 16{x^2} - 24xy + 9{y^2}\\ = \left( {9{x^2} + 16{x^2}} \right) + \left( {24xy - 24xy} \right) + \left( {16{y^2} + 9{y^2}} \right)\\ = 25{x^2} + 25{y^2}\end{array}\)