Question

Efectuati
a) (2√3+x)^2
b) (3√3x+2√5)^2
c) ( 1 supra 2 x + 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)

16 PUNCTE

Answer 1

$a).(2 \sqrt{3} +x)^2=(2 \sqrt{3} )^2+2*2 \sqrt{3} *x+x^2=12+4x \sqrt{3} +x^2 \\ b).(3 \sqrt{3} x+2 \sqrt{5} )^2=(3 \sqrt{3} x)^2+2*3 \sqrt{3} x*2 \sqrt{5} +(2 \sqrt{5} )^2= \\ =27x^2+12x \sqrt{15} +20 \\ c).( \frac{1}{2} x+3)^2= (\frac{1}{2} x)^2+2* \frac{1}{2} x*3+3^2= \frac{1}{4} x^2+ \frac{6}{2} x+9= \frac{x^2}{4} +3x+9 \\ d).(3-2 \sqrt{3} )^2=3^2-2*3*2 \sqrt{3} +(2 \sqrt{3} )^2= \\ =9-12 \sqrt{3} +12=21-12 \sqrt{3}$
$e).(2 \sqrt{5} x-3 \sqrt{2} x)^2=(2 \sqrt{5} x)^2-2*2 \sqrt{5} x*3 \sqrt{2} x+(3 \sqrt{2} x)^2= \\ =20x^2-12x^2 \sqrt{10} +18x^2=38x^2-12x^2 \sqrt{10} \\ f).(5 \sqrt{2} x-4 \sqrt{3} y)^2=(5 \sqrt{2} x)^2-2*5 \sqrt{2} x*4 \sqrt{3} y+(4 \sqrt{3} y)^2= \\ =50x^2-40 \sqrt{6} xy+48y^2 \\ g).(8x-4 \sqrt{5} )(8x+4 \sqrt{5} )=64x^2-80 \\ h).(7 \sqrt{2} a-5 \sqrt{6} b)(7 \sqrt{2} a+5 \sqrt{6} b)=98a^2-150b^2 \\ i).( \sqrt{2} x-3y)( \sqrt{2} x+3y)=2x^2-9y^2$