Question

Descompuneti in factori aplicand formula a *2 -b*2=(a+b) (a-b) :

A ) ( x + radical din 2 ) *2 - (2 radical din 2 ) *2
B) (x - radical din 5 ) *2 - (3- radical din 5)*3

Answer 1

A) $(x+ \sqrt{2} )^{2} - (2 \sqrt{2} )^{2} =(x+ \sqrt{2}+2 \sqrt{2})(x+ \sqrt{2} -2 \sqrt{2})$$=(x+3 \sqrt{2})(x- \sqrt{2} )$
B)$(x- \sqrt{5} )^{2}- (3- \sqrt{5} )^{2}=(x- \sqrt{5}+3- \sqrt{5})(x- \sqrt{5}-3+ \sqrt{5} )$$=(x+3-2 \sqrt{5})(x-3)$