[tex]6)a) {(2x - y)}^{2} = 4 {x}^{2} - 4xy + {y}^{2} [/tex]
[tex]b) {(3x - 2y)}^{2} = 9 {x}^{2} - 12xy + 4 {y}^{2} [/tex]
[tex]c) {( {x}^{3} - {y}^{3} )}^{2} = {x}^{6} - 2 {x}^{3} {y}^{3} + {y}^{6} [/tex]
[tex]d) {(2 {x}^{2} - {y}^{3} )}^{2} = 4 {x}^{4} - 4 {x}^{2} {y}^{3} + {y}^{6} [/tex]
[tex]e) {( {a}^{4} - 2 {b}^{3}) }^{2} = {a}^{8} - 4 {a}^{4} {b}^{3} + 4 {b}^{6} [/tex]
[tex]f) {(3 {a}^{2} - 2 {b}^{2}) }^{2} = 9 {a}^{4} - 12 {a}^{2} {b}^{2} + 4 {b}^{4} [/tex]
[tex]g) { ({x}^{4} - 3 {y}^{3} )}^{2} = {x}^{8} - 6 {x}^{4} {y}^{3} + 9 {y}^{6} [/tex]
[tex]h) {( {a}^{9} - 3 {b}^{6}) }^{2} = {a}^{18} - 6 {a}^{9} {b}^{6} + 9 {b}^{12} [/tex]
[tex]i) {(3b - {a}^{4} )}^{2} = 9 {b}^{2} - 6b {a}^{4} + {a}^{8} [/tex]
[tex]j) {(2 {x}^{3} - 3 {y}^{2}) }^{2} = 4 {x}^{6} - 12 {x}^{3} {y}^{2} + 9 {y}^{4} [/tex]
[tex]k) {(3 {x}^{3} - a)}^{2} = 9 {x}^{6} - 6 {x}^{3} a + {a}^{2} [/tex]
[tex]l) {(2 {y}^{5} - 3 {b}^{8} )}^{2} = 4 {y}^{10} - 12 {y}^{5} {b}^{8} + 9 {b}^{16} [/tex]
[tex]8)a) {( \sqrt{3} - \sqrt{5} )}^{2} = 3 - 2 \sqrt{15} + 5 = 8 - 2 \sqrt{15} = 2(4 - \sqrt{15} )[/tex]
[tex]b) {( \sqrt{3} - 1)}^{2} = 3 - 2 \sqrt{3} + 1 = 4 - 2 \sqrt{3} = 2(2 - \sqrt{3} )[/tex]
[tex]c) {(3 \sqrt{3} - 2)}^{2} = 27 - 12 \sqrt{3} + 4 = 31 - 12 \sqrt{3} [/tex]
[tex]d) {(3 \sqrt{3} - 2 \sqrt{2}) }^{2} = 27 - 12 \sqrt{6} + 8 = 35 - 12 \sqrt{6} [/tex]
[tex]e) {( \sqrt{8} - \sqrt{2} )}^{2} = 8 - 2 \sqrt{16} + 2 = 10 - 2 \times 4 = 10 - 8 = 2[/tex]
[tex]f) {(7 \sqrt{3} - 3 \sqrt{2}) }^{2} = 147 - 42 \sqrt{6} + 18 = 165 - 42 \sqrt{6} = 3(55 - 14 \sqrt{6} )[/tex]
[tex]g) {(4 \sqrt{2} - 3 \sqrt{3} )}^{2} = 32 - 24 \sqrt{6} + 27 = 59 - 24 \sqrt{6} [/tex]
