Question

ex 7 punctele a,b,c si d ; ex 8 punctele a,d si ex 9 punctele a si c va rog ...dau coroana

Answer 1

7)a)
$( 3x + \sqrt{2)}^{2} = \\ {(3x)}^{2} + 2 \times 3x \times \sqrt{2} + { \sqrt{2} }^{2} = \\ {9x}^{2} + 6x \sqrt{2} + 2$
B)
$(2x - \sqrt{3})^{2} = \\ {(2x)}^{2} - 2 \times 2x \times \sqrt{3} + \sqrt{3} ^{2} = \\ 4 {x}^{2} - 4x \sqrt{3} + 3$
C)
$(2x + 3 \sqrt{2} )^{2} = \\ (2x) ^{2} + 2 \times 2x \times 3 \sqrt{2} + (3 \sqrt{2)} ^{2} = \\ {4x}^{2} + 12x \sqrt{2} + 18$
D)
$(3x - \sqrt{3} )^{2} = \\ ( {3x)}^{2} - 2 \times 3x \times \sqrt{3} + { \sqrt{3} }^{2} = \\ 9 {x}^{2} - 6x \sqrt{3} + 3$

8)a)
${(1 + x)}^{2} + {(2 + x)}^{2} + {(3 + x)}^{2} =$
${1}^{2} + 2x + {x}^{2} + {2}^{2} + 4x + {x}^{2} + \\ {3}^{2} + 6x + {x}^{2} =$
$1 + 2x + {x}^{2} + 4 + 4x + {x}^{2} + \\ 9 + 6x + {x}^{2} =$
$3 {x}^{2} + 12x + 14$
D)
$(2x + 3y) ^{2} + (2x + 3y)(2x - 3y)$

$4 {x}^{2} + 2 \times 2x \times 3y + 9 {y}^{2} + \\ {(2x)}^{2} - {(3y)}^{2} =$
$4 {x}^{2} + 12xy + 9 {y}^{2} + 4 {x}^{2} - 9 {y}^{2} = \\ 8 {x}^{2} + 12xy$

9)a)
${(x - 3)}^{2} + {(x + 1)}^{2} - \\ (2x + 1)(2x - 1) =$

${x}^{2} - 6x + 9 + {x}^{2} + 2x + 1 - \\ (4 {x}^{2} - 1) =$
$2 {x}^{2} - 4x + 10 - 4 {x}^{2} + 1 = \\ - 2 {x}^{2} - 4x + 11$

C)
${(x + 4)}^{2} -(2x - 3)(2x + 3) + \\ {(2x + 1)}^{2} =$


${x }^{2} + 8x + 16 - (4 {x}^{2} - 9) + \\ 4 {x}^{2} + 4x + 1 =$

${x }^{2} + 8x + 16 - 4 {x}^{2} + 9 + \\ 4 {x}^{2} + 4x + 1 =$


${x}^{2} + 12x + 26$