Answer:
[tex] {(2x + y)}^{2} - {(x - 2y)}^{2} [/tex]
[tex] < {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} > [/tex]
[tex] < {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} > [/tex]
[tex] {(2x)}^{2} + 2(2x)(y) + {(y)}^{2} - {(x)}^{2} - 2(x)(2y) + {(2y)}^{2} [/tex]
[tex] {4x}^{2} + 4xy + {y}^{2} - {x}^{2} - 4xy + {4y}^{2} [/tex]
[tex] {4x}^{2} - {x}^{2} + {4y}^{2} + {y}^{2} [/tex]
[tex] = {3x}^{2} + {5y}^{2} [/tex]
