7)a)
[tex]( 3x + \sqrt{2)}^{2} = \\ {(3x)}^{2} + 2 \times 3x \times \sqrt{2} + { \sqrt{2} }^{2} = \\ {9x}^{2} + 6x \sqrt{2} + 2[/tex]
B)
[tex](2x - \sqrt{3})^{2} = \\ {(2x)}^{2} - 2 \times 2x \times \sqrt{3} + \sqrt{3} ^{2} = \\ 4 {x}^{2} - 4x \sqrt{3} + 3[/tex]
C)
[tex](2x + 3 \sqrt{2} )^{2} = \\ (2x) ^{2} + 2 \times 2x \times 3 \sqrt{2} + (3 \sqrt{2)} ^{2} = \\ {4x}^{2} + 12x \sqrt{2} + 18[/tex]
D)
[tex](3x - \sqrt{3} )^{2} = \\ ( {3x)}^{2} - 2 \times 3x \times \sqrt{3} + { \sqrt{3} }^{2} = \\ 9 {x}^{2} - 6x \sqrt{3} + 3[/tex]
8)a)
[tex] {(1 + x)}^{2} + {(2 + x)}^{2} + {(3 + x)}^{2} = [/tex]
[tex] {1}^{2} + 2x + {x}^{2} + {2}^{2} + 4x + {x}^{2} + \\ {3}^{2} + 6x + {x}^{2} = [/tex]
[tex]1 + 2x + {x}^{2} + 4 + 4x + {x}^{2} + \\ 9 + 6x + {x}^{2} = [/tex]
[tex]3 {x}^{2} + 12x + 14[/tex]
D)
[tex](2x + 3y) ^{2} + (2x + 3y)(2x - 3y)[/tex]
[tex]4 {x}^{2} + 2 \times 2x \times 3y + 9 {y}^{2} + \\ {(2x)}^{2} - {(3y)}^{2} = [/tex]
[tex]4 {x}^{2} + 12xy + 9 {y}^{2} + 4 {x}^{2} - 9 {y}^{2} = \\ 8 {x}^{2} + 12xy [/tex]
9)a)
[tex] {(x - 3)}^{2} + {(x + 1)}^{2} - \\ (2x + 1)(2x - 1) = [/tex]
[tex] {x}^{2} - 6x + 9 + {x}^{2} + 2x + 1 - \\ (4 {x}^{2} - 1) = [/tex]
[tex]2 {x}^{2} - 4x + 10 - 4 {x}^{2} + 1 = \\ - 2 {x}^{2} - 4x + 11[/tex]
C)
[tex] {(x + 4)}^{2} -(2x - 3)(2x + 3) + \\ {(2x + 1)}^{2} = [/tex]
[tex] {x }^{2} + 8x + 16 - (4 {x}^{2} - 9) + \\ 4 {x}^{2} + 4x + 1 = [/tex]
[tex] {x }^{2} + 8x + 16 - 4 {x}^{2} + 9 + \\ 4 {x}^{2} + 4x + 1 = [/tex]
[tex] {x}^{2} + 12x + 26[/tex]
