Question

Wyznacz wielomiany f(x)= u(x)- [w(x)]do kwadratu oraz g(x)=u(x)*[w(x)]do kwadratu.

a) u(x)= 4x²+4x+1, w(x)=2x-1

b)u(x)= x²-2x+1, w(x)=x²+x

c)u(x)= x⁴-1, w(x)=1-x²

z góry dzięki:))

Answer 1

A) f(x)=(4x^2+4x+1)-(2x-1)^2
f(x)= 4x^2+4x+1-4x^2+4x-1= 8x
g(x)=(4x^2+4x+1)(4x^2-4x+1)
g(x)=16x^4-8x^2+1
b)
f(x)=(x^2-2x+1)-(x^4+2x^3+x^2)
f(x)= -x^4-2x^2-2x+1
g(x)=(x^2-2x+1)(x^4+2x^3+x^2)
g(x)=x^6+2x^5-2x^4+x^2
c)
f(x)= (x^4-1)-(1-x^2)
f(x)= 2x^2-2
g(x)= (x^4-1)(x^4-2x^2+1)
g(x)=x^8-2x^6+2x^2-1
^- do potęgi jakiejś tam