W(x)=4x^3-2x^2+x-2 , P(x)=x^3+3x+1 , Q(x)=2x^4+x^3-x+6
d)
minus przed nawiasem zmienia znaki w nawiasie na przeciwne
Q(x)-2W(x)-P(x)=
=2x^4+x^3-x+6-2(4x^3-2x^2+x-2)-(x^3+3x+1)=
=2x^4+x^3-x+6-8x^3+4x^2-2x+4-x^3-3x-1=
=2x^4-8x^3+4x^2-6x+9
e)
P(x)*[W(x)-Q(x)]=
=(x^3+3x+1)*[(4x^3-2x^2+x-2)-(2x^4+x^3-x+6)]=
=(x^3+3x+1)*(4x^3-2x^2+x-2-2x^4-x^3+x-6)=
=(x^3+3x+1)*(-2x^4+3x^3-2x^2+2x-8)=
=-2x^7+3x^6-2x^5+2x^4-8x^3-6x^5+9x^4-6x^3+6x^2-24x-2x^4+3x^3-2x^2+2x-8=
=-2x^7+3x^6-8x^5+9x^4-11x^3+4x^2-22x-8
f)
[P(x)]^2-Q(x)-W(x)=
=(x^3+3x+1)^2-(2x^4+x^3-x+6)-(4x^3-2x^2+x-2)=
=x^6+9x^2+1+2*3x^4+2*3x+2x^3-2x^4-x^3+x-6-4x^3+2x^2-x+2=
=x^6+4x^4-3x^3+11x^2+6x-3
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(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac