Formule de calcul prescurtat
[tex](x + y) ^{2} = {x}^{2} + 2 \times x \times y + {y}^{2} [/tex]
[tex](x - y) ^{2} = {x}^{2} - 2 \times x \times y + {y}^{2} [/tex]
[tex](x - y)(x + y) = {x}^{2} - {y}^{2} [/tex]
E)
[tex]4a^{2} + 4ab + {b}^{2} - \\ (4 {a}^{2} - 4ab + {b}^{2} ) - ( {9a}^{2} - {b}^{2} ) = [/tex]
[tex]4 {a}^{2} + 4ab + {b}^{2} - {4a}^{2} + 4ab \\ - {b}^{2} - {9a}^{2} + {b}^{2} = [/tex]
[tex] - {9a}^{2} + 8ab + {b}^{2} [/tex]
F)
[tex]9 - 12a + {4a}^{2} - \\ ( {16a}^{2} + 8a + 1) + {16a}^{2} - 25 = [/tex]
[tex]9 - 12a + 4 {a}^{2} - 16 {a}^{2} - 8a - 1 \\ + 16 {a}^{2} - 25 = [/tex]
[tex]4 {a}^{2} - 20a - 17[/tex]
G)
[tex](3 + 4a \sqrt{3} + {4a}^{2} - \\ ( {a}^{2} + 4a \sqrt{3} + 12)) ^{2} = [/tex]
[tex](3 + 4a \sqrt{3} + 4 {a}^{2} - {a}^{2} - \\ 4a \sqrt{3} - 12) ^{2} [/tex]
[tex](3 {a}^{2} - 9) ^{2} = [/tex]
[tex]9 {a}^{4} - 54 {a}^{2} + 81[/tex]