Question

Daca x= 3 x a + 2 x b si y= 2 x a +3 x b , unde a ,b ∈ N si a > b , aratati ca (x +y ) x ( x - y )≡ ( a + b) x ( a - b )

Answer 1

(x+y)(x-y)=(3a+2b+2a+3b)(3a+2b-2a-3b)=(5a+5b)(a-b)=5(a+b)(a-b)=>
(x+y)(x-y)$\vdots$(a+b)(a-b)