Znajdź różnicę wielomianów \( W(x) \) i \( U(x) \), jeśli:
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a) \( W(x)=2x^3-4x^2+x-2 \), \( U(x)=-3x^3-4x^2+2x \)
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b) \( W(x)=2+x-4x^3+2x^4 \), \( U(x)=-1+3x+4x^2+x^4 \)
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Różnica wielomianów \( W(x) \) i \( U(x) \) to \( W(x)-U(x) \). Policzymy to zatem
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a) \( W(x)=2x^3-4x^2+x-2 \), \( U(x)=-3x^3-4x^2+2x \)
\[
W(x)-U(x)=2x^3-4x^2+x-2-(-3x^3-4x^2+2x)=\\
=\class{color3}{2x^3}
\class{color2}{-4x^2}\class{color1}{+x}-2\class{color3}{+3x^3}\class{color2}{+4x^2}
\class{color1}{+2x}=\class{color3}{5x^3}\class{color1}{+3x}-2
\]
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b) \( W(x)=2+x-4x^3+2x^4 \), \( U(x)=-1+3x+4x^2+x^4 \)
\[
W(x)-U(x)=2+x-4x^3+2x^4-(-1+3x+4x^2+x^4)=\\
=
2+\class{color1}{x}\class{color3}{-4x^3}\class{color4}{2x^4}+1\class{color1}{-3x}
\class{color2}{+4x^2}\class{color4}{+x^4}=
\class{color4}{x^4}\class{color3}{-4x^3}\class{color2}{-4x^2}\class{color1}{-2x}+3
\]
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