Question

Scrieti ca produs de trei factori:
a) x^3-xy^2
b)a(x+1)^2-a(x-1)^2
c)(x^2+7)^2-16(x^2+7)
d)(x^2+x+1)^2-1
e)(a^2+b^2)^2-4a^2b^2

Answer 1

a) x³-xy²=x(x²-y²)=x(x-y)(x+y)
b)a(x+1)²-a(x-1)²=a[(x+1)²-(x-1)²]=a(x+1-x+1)(x+1+x-1)=a×2×2x=4ax
c)(x²+7)²-16(x²+7)²=(x²+7)(x²+7-16)=(x²+7)(x²-9)=(x²+7)(x-3)(x+3)
d)(x²+x+1)²-1=(x²+x+1-1)(x²+x+1+1)=(x²+x)(x²+x+2)=x(x+1)((x²+x+2)
e)(a²+b²)²-4a²b² =(a²+b²-2ab)(a²+b²+2ab) =(a-b)²(a+b)² =(a-b)(a+b)(a²-b²)