Răspuns:
[tex]23)a)a(a - 3) + (a + 3)(a + 2) - {(a - 2)}^{2} = \\ = {a}^{2} - 3a + {a}^{2} + 2a + 3a + 6 - ( {a}^{2} - 4a + 4) = \\ = 2 {a}^{2} + 2a + 6 - {a}^{2} + 4a - 4 = {a}^{2} + 6a + 2[/tex]
[tex]b) {(x - 1)}^{2} - (x - 1)(x + 1) + {(x + 1)}^{2} = \\ = {x}^{2} - 2x + 1 - ( {x}^{2} - 1) + {x}^{2} + 2x + 1 = \\ = {x}^{2} - 2x + 1 - {x}^{2} + 1 + {x}^{2} + 2x + 1 = \\ = {x}^{2} + 3[/tex]
[tex]c) {(m + 3)}^{2} + {(m - 3)}^{2} - 2(m - 3)(m + 3) = \\ {m}^{2} + 6m + 9 + {m}^{2} - 6m + 9 - 2( {m}^{2} - {3}^{2} ) = \\ = 2 {m}^{2} + 18 - 2( {m}^{2} - 9) = \\ = 2 {m}^{2} + 18 - 2 {m}^{2} + 18 = 36[/tex]
[tex]d) {(a - b)}^{2} - {(a + b)}^{2} - (a - b)(a + b) = \\ = {a}^{2} - 2ab + {b}^{2} - ( {a}^{2} + 2ab + {b}^{2}) - ( {a}^{2} - {b}^{2} ) = \\ = {a}^{2} - 2ab + {b}^{2} - {a}^{2} - 2ab - {b}^{2} - {a}^{2} + {b}^{2} = \\ = - {a}^{2} + {b}^{2} - 4ab[/tex]
