[tex](a + 1)(a - b) = {a}^{2} - ab + a - b[/tex]
[tex] - (a + 1)(a - b) = (a + 1)(b - a) = ab - {a}^{2} + b - a = - {a}^{2} + ab - a + b[/tex]
[tex] - (4x + 1)(x - 3) = (4x + 1)(3 - x) = 12x - 4 {x}^{2} + 3 - x = \\ \\ = - 4 {x}^{2} + 11x + 3[/tex]
[tex] - (4 - y)(y - 11) = (y - 4)(y - 11) = {y}^{2} - 11y - 4y + 44 = \\ \\ = {y}^{2} - 15y + 44[/tex]
[tex] - (x - y)( {x}^{2} + {y}^{2} ) = (y - x)( {x}^{2} + {y}^{2} ) = {x}^{2} y + {y}^{3} - {x}^{3} - x {y}^{2} = \\ \\ = - {x}^{3} - x {y}^{2} + {x}^{2} y + {y}^{3} [/tex]
[tex] - (2 {m}^{2} - 2 {n}^{2} )( {m}^{2} + {n}^{2} ) = (2 {n}^{2} - 2 {m}^{2} )( {m}^{2} + {n}^{2} ) = \\ \\ = 2 {n}^{2} {m}^{2} + 2 {n}^{4} - 2 {m}^{4} - 2 {m}^{2} {n}^{2} = 2 {n}^{4} - 2 {m}^{4} [/tex]
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[tex](a + 1)(a - b) = {a}^{2} - ab + a - b[/tex]
[tex] - (a + 1)(a - b) = (a + 1)(b - a) = ab - {a}^{2} + b - a = - {a}^{2} + ab - a + b[/tex]
[tex] - (4x + 1)(x - 3) = (4x + 1)(3 - x) = 12x - 4 {x}^{2} + 3 - x = \\ \\ = - 4 {x}^{2} + 11x + 3[/tex]
[tex] - (4 - y)(y - 11) = (y - 4)(y - 11) = {y}^{2} - 11y - 4y + 44 = \\ \\ = {y}^{2} - 15y + 44[/tex]
[tex] - (x - y)( {x}^{2} + {y}^{2} ) = (y - x)( {x}^{2} + {y}^{2} ) = {x}^{2} y + {y}^{3} - {x}^{3} - x {y}^{2} = \\ \\ = - {x}^{3} - x {y}^{2} + {x}^{2} y + {y}^{3} [/tex]
[tex] - (2 {m}^{2} - 2 {n}^{2} )( {m}^{2} + {n}^{2} ) = (2 {n}^{2} - 2 {m}^{2} )( {m}^{2} + {n}^{2} ) = \\ \\ = 2 {n}^{2} {m}^{2} + 2 {n}^{4} - 2 {m}^{4} - 2 {m}^{2} {n}^{2} = 2 {n}^{4} - 2 {m}^{4} [/tex]