Question

Exercitiile 6 si 8 va rog frumos ajutor

Answer 1

$6)a) {(2x - y)}^{2} = 4 {x}^{2} - 4xy + {y}^{2}$

$b) {(3x - 2y)}^{2} = 9 {x}^{2} - 12xy + 4 {y}^{2}$

$c) {( {x}^{3} - {y}^{3} )}^{2} = {x}^{6} - 2 {x}^{3} {y}^{3} + {y}^{6}$

$d) {(2 {x}^{2} - {y}^{3} )}^{2} = 4 {x}^{4} - 4 {x}^{2} {y}^{3} + {y}^{6}$

$e) {( {a}^{4} - 2 {b}^{3}) }^{2} = {a}^{8} - 4 {a}^{4} {b}^{3} + 4 {b}^{6}$

$f) {(3 {a}^{2} - 2 {b}^{2}) }^{2} = 9 {a}^{4} - 12 {a}^{2} {b}^{2} + 4 {b}^{4}$

$g) { ({x}^{4} - 3 {y}^{3} )}^{2} = {x}^{8} - 6 {x}^{4} {y}^{3} + 9 {y}^{6}$

$h) {( {a}^{9} - 3 {b}^{6}) }^{2} = {a}^{18} - 6 {a}^{9} {b}^{6} + 9 {b}^{12}$

$i) {(3b - {a}^{4} )}^{2} = 9 {b}^{2} - 6b {a}^{4} + {a}^{8}$

$j) {(2 {x}^{3} - 3 {y}^{2}) }^{2} = 4 {x}^{6} - 12 {x}^{3} {y}^{2} + 9 {y}^{4}$

$k) {(3 {x}^{3} - a)}^{2} = 9 {x}^{6} - 6 {x}^{3} a + {a}^{2}$

$l) {(2 {y}^{5} - 3 {b}^{8} )}^{2} = 4 {y}^{10} - 12 {y}^{5} {b}^{8} + 9 {b}^{16}$

$8)a) {( \sqrt{3} - \sqrt{5} )}^{2} = 3 - 2 \sqrt{15} + 5 = 8 - 2 \sqrt{15} = 2(4 - \sqrt{15} )$

$b) {( \sqrt{3} - 1)}^{2} = 3 - 2 \sqrt{3} + 1 = 4 - 2 \sqrt{3} = 2(2 - \sqrt{3} )$

$c) {(3 \sqrt{3} - 2)}^{2} = 27 - 12 \sqrt{3} + 4 = 31 - 12 \sqrt{3}$

$d) {(3 \sqrt{3} - 2 \sqrt{2}) }^{2} = 27 - 12 \sqrt{6} + 8 = 35 - 12 \sqrt{6}$

$e) {( \sqrt{8} - \sqrt{2} )}^{2} = 8 - 2 \sqrt{16} + 2 = 10 - 2 \times 4 = 10 - 8 = 2$

$f) {(7 \sqrt{3} - 3 \sqrt{2}) }^{2} = 147 - 42 \sqrt{6} + 18 = 165 - 42 \sqrt{6} = 3(55 - 14 \sqrt{6} )$

$g) {(4 \sqrt{2} - 3 \sqrt{3} )}^{2} = 32 - 24 \sqrt{6} + 27 = 59 - 24 \sqrt{6}$