Question

Descompuneti in factori

Answer 1

$c).(x+ \sqrt{2} )^2-8=(x+ \sqrt{2} )-2 \sqrt{2} = \\ = (x+ \sqrt{2} -2 \sqrt{2} )(x+ \sqrt{2} +2 \sqrt{2} )=(x- \sqrt{2} )(x+3 \sqrt{2} ) \\ d).(2x+ \sqrt{3} )^2-27=(2x+ \sqrt{3} )-3 \sqrt{3} = \\ =(2x+ \sqrt{3} -3 \sqrt{3} )(2x+ \sqrt{3} + 3\sqrt{3} )=(2x-2 \sqrt{3} )(2x+4 \sqrt{3} )= \\ =2(x- \sqrt{3} ) \cdot 2(x+2 \sqrt{3} )=4(x- \sqrt{3} )(x+2 \sqrt{3} )$
$e).( \sqrt{2} x-1)^2-32x^2=( \sqrt{2} x-1)^2-4 \sqrt{2} x= \\ =(\sqrt{2} x-1-4 \sqrt{2} x)( \sqrt{2} x-1+4 \sqrt{2} x)=(-3 \sqrt{2} x-1)(5 \sqrt{2} x-1)$
$f).a^6-b^6=(a^3-b^3)(a^3+b^3)= \\ =(a-b)(a^2+ab+b^2)(a+b)(a^2-ab+b^2)$
$g).x^2-2 \sqrt{3} x+3-(y-2 \sqrt{3} )^2=(x- \sqrt{3} )^2-(y-2 \sqrt{3} )^2= \\ =[(x- \sqrt{3} )-(y-2 \sqrt{3} )][(x- \sqrt{3} )+(y-2 \sqrt{3} )]= \\ =(x- \sqrt{3} -y+2 \sqrt{3} )(x- \sqrt{3} +y-2 \sqrt{3} )= \\ =(x-y+ \sqrt{3} )(x+y-3 \sqrt{3} )$
$h).14a-49a^2+100b^2-1=7a(2-7a)+(10b-1)(10b+1)$