Question

Dau coronaa! scrieti ca produs de 3 factori : x³-xy² , a(x+1)²-a(x-1)² , (x²+7)²-16(x²+7) , (x²+x+1)²-1 , (a²+b²)²-4a²b²

Answer 1

x³-xy²=x(x²-y²)=x(x-y)(x+y)


a(x+1)²-a(x-1)²=a(x+1)²-a(x-1)(x+1)=(x+1)[a(x+1)-a(x-1)]=(x+1)×a(x+1-x+1)
=(x+1)×a×2


(x²+7)²-16(x²+7)=(x²+7)(1-16)=(x²+7)(1-4)(1+4)=(x²+7)×(-3)×5

(x²+x+1)²-1 =(x²+x+1+1)(x²+x+1-1)=(x²+x+2)[(x+1)²-1]=(x²+x+2)(x+1-1)(x+1+1)=(x²+x+2)×x(x+2)

(a²+b²)²-4a²b²=[(a²+b²)-2ab][a²+b²+2ab]=(a-b)²(a+b)²=(a-b)(a-b)(a+b)²