a) $A(x)+B(x)+C(x)=A(x)+(B(x)+C(x))=2x^{3}-2x^{2}+x-4+(3x^{3}-2x+3-x^{3}+1)=2x^{3}-2x^{2}+x-4+2x^{3}-2x+4=4x^{3}-2x^{2}-x$
b) $A(x)-B(x)-C(x)=A(x)-(B(x)+C(x))=2x^{3}-2x^{2}+x-4-(3x^{3}-2x+3-x^{3}+1)=2x^{3}-2x^{2}+x-4-2x^{3}+2x-4=-2x^{2}+3x-8$
Bài 7.18. Cho các đa thức $A(x) =2x^{3}-2x^{2}+x-4;B=3x^{3}-2x+3$ và $C(x)=-x^{3}+1$. Hãy tính:
a) A(x) + B(x) + C(x)
b) A(x) - B (x) - C(x)
a) $A(x)+B(x)+C(x)=A(x)+(B(x)+C(x))=2x^{3}-2x^{2}+x-4+(3x^{3}-2x+3-x^{3}+1)=2x^{3}-2x^{2}+x-4+2x^{3}-2x+4=4x^{3}-2x^{2}-x$
b) $A(x)-B(x)-C(x)=A(x)-(B(x)+C(x))=2x^{3}-2x^{2}+x-4-(3x^{3}-2x+3-x^{3}+1)=2x^{3}-2x^{2}+x-4-2x^{3}+2x-4=-2x^{2}+3x-8$