Câu 1: các biểu thức sau không phụ thuộc vào biến đúng hay sai:
\(A.2\left(2x+x^2\right)-x^2\left(x+2\right)+\left(x^3-4x+3\right)\)
B. \(x\left(x^2+x+1\right)-x^2\left(x+1\right)-x+5\)
C. \(3x\left(x-2\right)-5x\left(x-1\right)-8\left(x^2-3\right)\)
D. \(2y\left(y^2+y+1\right)-2y^2\left(y+1\right)-2\left(y+10\right)\)
* Trình bày cách làm
\(A.2\left(2x+x^2\right)-x^2\left(x+2\right)+\left(x^3-4x+3\right)\)
\(=4x+2x^2-x^3-2x^2+x^3-4x+3\)
\(=3\)
\(\Rightarrow A:\) đúng.
\(B.x\left(x^2+x+1\right)-x^2\left(x+1\right)-x+5\)
\(=x^3+x^2+x-x^2\left(x+1\right)-x-1+6\)
\(=x^3+x\left(x+1\right)-x^2\left(x+1\right)-\left(x+1\right)+6\)
\(=x^3+\left(x+1\right)\left(x-x^2-1\right)+6\)
\(=x^3+x^2+x-x^3-x^2-x-1+6\)
\(=5\)
\(\Rightarrow B:\) đúng.
\(C.3x\left(x-2\right)-5x\left(x-1\right)-8\left(x^2-3\right)\)
\(=3x^2-6x-5x^2+5x-8x^2+24\)
\(=-10x^2-x+24\)
\(\Rightarrow C:sai.\)
\(D.2y\left(y^2+y+1\right)-2y^2\left(y+1\right)-2\left(y+10\right)\)
\(=2y^3+2y+2y-2y^3-2y^2-2y-20\)
\(=-2y^2+2y-20\)
\(\Rightarrow D:sai.\)