Question

Efectuati:
a) (2√3+x)²=
b) (3√3x+2√5)²=
c) (½x+3)²=
d) (3-2√3)²=
e) (2√5x-3√2x)²=
f) (5√2x-4√3y)²=
g) (8x-4√5)(8x+4√5)=
h) (7√2a-5√6b)(7√2a+5√6b)=
i) (√2x-3y)(√2x+3y)=
j) (⅓x-3\2)²=
k) (√2/2x+1\√2y)²=
l) (⅓x-5/6yz)(⅓x+5/6yz)=
m) (x-3)(x+3)(x²+9)-(x²+9)-(x²+2)²+3(x-1)²=
n) (x+5)(x²-1)-x(x+4)²+(x-1)²=
o) (3xy-5)(3xy+5)-(3xy-2)²=
p) (5x-8)[2(x+1)+3(x+2)]-(3x-4)[5(x+2)-2(x+3)]=
q) (7√3+√2)²-2(1+7√6)=
r) 2√5(√3-1)+(√5-√3)²=
s) 12√75+(6-5√3)²=
ș) (3√7-2√6)²+60√126:(5√3)=
t) (3√5-√15)(3√5+√15)-2(√6+1)²=

Answer 1

$a).(2 \sqrt{3} +x)^2=(2 \sqrt{3} )^2+2*2 \sqrt{3} *x+x^2=12+4x \sqrt{3} +x^2 \\ b).(3 \sqrt{3} x+ 2\sqrt{5} )^2=(3 \sqrt{3} x)^2+2*3 \sqrt{3} x*2 \sqrt{5} +(2 \sqrt{5} )^2= \\ =27x^2+12x \sqrt{15} +20 \\ c).( \frac{1}{2} x+3)^2=( \frac{1}{2} x)^2+2* \frac{1}{2} x*3+3^2= \frac{1}{4} x^2+ \frac{6x}{2} +9= \frac{1}{4} x^2+3x+9$
$d).(3-2 \sqrt{3} )^2=3^2+2*3*2 \sqrt{3} +(2 \sqrt{3} )^2=9+12 \sqrt{3} +12= \\ =21+12 \sqrt{3} \\ e).(2 \sqrt{5} x-3 \sqrt{2} x)^2=(2 \sqrt{5} x)^2-2*2 \sqrt{5} x*3 \sqrt{2} x+(3 \sqrt{2} x)^2= \\ =20x^2-12x^2 \sqrt{10} +18x^2=38x^2-12x^2 \sqrt{10} \\ f).(5 \sqrt{2} x-4 \sqrt{3} y)^2=(5 \sqrt{2} x)^2-2*5 \sqrt{2} x*4 \sqrt{3} y+(4 \sqrt{3} y)^2= \\ =50x^2-40xy \sqrt{6} +48y^2$$g).(8x-4 \sqrt{5} )(8x+4 \sqrt{5} )=64x^2-80 \\ h).(7 \sqrt{2} a-5 \sqrt{6} b)(7 \sqrt{2} a+5 \sqrt{6} b)=98a^2-150b^2$
$i).( \sqrt{2} x-3y)( \sqrt{2} x+3y)=2x^2-9y^2 \\ j).( \frac{1}{3} x- \frac{3}{2} )^2=( \frac{1}{3} x)^2-2* \frac{1}{3} x* \frac{3}{2} +( \frac{3}{2} )^2= \frac{1}{9} x^2- \frac{6}{6} x+ \frac{9}{4} = \\ = \frac{1}{9} x^2-x+ \frac{9}{4} \\ k). ( \frac{ \sqrt{2} }{2} x+ \frac{1}{ \sqrt{2} }y )= (\frac{ \sqrt{2} }{2} x)^2+2* \frac{ \sqrt{2} }{2} x* \frac{1}{ \sqrt{2} } y+( \frac{1}{ \sqrt{2} }y )^2= \\ = \frac{2}{4} x^2+ \frac{2 \sqrt{2} }{2 \sqrt{2} } xy+ \frac{1}{2} y^2= \frac{2}{4} x^2+xy+ \frac{1}{2} y^2$
$l).( \frac{1}{3} x- \frac{5}{6} yz)( \frac{1}{3} x+ \frac{5}{6} yz)= \frac{1}{9} x^2- \frac{25}{36} y^2z^2$
$m).(x-3)(x+3)(x^2+9)-(x^2+9)-(x^2+2)^2+3(x-1)^2= \\ =(x^2-9)(x^2+9)-(x^2-9)-(x^4+4x^2+4)+3(x^2-2x+1)= \\ =x^4-81-x^2+9-x^4-4x^2-4+3x^2-6x+3= -2x^2-6x-73$
$n).(x+5)(x^2-1)-x(x+4)^2+(x-1)^2= \\ =x^3-x+5x^2-5-x(x^2+2*x*4+4^2)+x^2-2*x*1+1^2= \\ =x^3-x+5x^2-5-x(x^2+8x+16)+x^2-2x+1= \\ =x^3-x+5x^2-5-x^3-8x^2-16x+x^2-2x+1=-2x^2-19x-4$
$o).(3xy-5)(3xy+5)-(3xy-2)^2= \\ =9x^2y^2-25-[(3xy)^2-2*3xy*2+2^2]= \\ =9x^2y^2-25-(9x^2y^2-12xy+4)=9x^2y^2-25-9x^2y^2+12xy-4= \\ =12xy-29$
$p).(5x-8)[2(x+1)+3(x+2)]-(3x-4)[5(x+2)-2(x+3)]= \\ =(5x-8)(2x+2+3x+6)-(3x-4)(5x+10-2x-6)= \\ =(5x-8)(5x+8)-(3x-4)(3x+4)=25x^2-64-9x^2+16= \\ =16x^2-48$
$q).(7 \sqrt{3} + \sqrt{2} )^2-2(1+7 \sqrt{6} )= \\ =(7 \sqrt{3} )^2+2*7 \sqrt{3} * \sqrt{2} + \sqrt{2} ^2-2-14 \sqrt{6} = \\ =147+14 \sqrt{6} +2-2-14 \sqrt{6} =147$
$r).2 \sqrt{5} ( \sqrt{3} -1)+( \sqrt{5} - \sqrt{3} )=2 \sqrt{15} -2 \sqrt{5} + \sqrt{5} + \sqrt{3} = \\ =2 \sqrt{15} - \sqrt{5} + \sqrt{3}$
$s).12 \sqrt{75} +(6-5 \sqrt{3} )^2=12*5 \sqrt{3} +6^2-2*6*5 \sqrt{3} +(5 \sqrt{3} )^2= \\ =60 \sqrt{3} +36-60 \sqrt{3} +75=111$
$t).(3 \sqrt{7}-2 \sqrt{6} )^2+60 \sqrt{126} :(5 \sqrt{3} )= \\ =(3 \sqrt{7} )^2-2*3 \sqrt{7} *2 \sqrt{6}+12 \sqrt{42} =63-12 \sqrt{42} +12 \sqrt{42} =63$
$u).(3 \sqrt{5} - \sqrt{15} )(3 \sqrt{5} + \sqrt{15} )-2( \sqrt{6} +1)^2= \\ =45-15-2( \sqrt{6} ^2+2* \sqrt{6} *1+1^2)=45-15-2(6+2 \sqrt{6} +1)= \\ =45-15-12-4 \sqrt{6} -2=16-4 \sqrt{6}$