Bài 1:
a) \(\left(x-1\right)\left(x^3+x^2+x+1\right)\)
\(=x^4+x^3+x^2+x-x^3-x^2-x-1\)
\(=x^4-1\)
b) \(\left(x-2\right)\left(x^2+x+1\right)-x\left(x^2-1\right)\)
\(=x^3+x+x-2x^2-2x-2-x^3+x\)
\(=-x^2-2\)
Bài 2:
a) \(\left(x+1\right)\left(x+2\right)+\left(1-x\right)\left(x-2\right)=7\) (1)
\(\Leftrightarrow x^2+2x+x+2+x-2-x^2+2x=7\)
\(\Leftrightarrow6x=7\)
\(\Leftrightarrow x=\dfrac{7}{6}\)
Vậy tập nghiệm phương trình (1) là \(S=\left\{\dfrac{7}{6}\right\}\)
b) \(\left(x+2\right)\left(x+3\right)-\left(x-3\right)\left(x+4\right)=5\)(2)
\(\Leftrightarrow x^2+3x+2x+6-\left(x^2+4x-3x-12\right)=5\)
\(\Leftrightarrow x^2+3x+2x+6-\left(x^2+x-12\right)=5\)
\(\Leftrightarrow x^2+3x+2x+6-x^2-x+12=5\)
\(\Leftrightarrow4x+18=5\)
\(\Leftrightarrow4x=5-18\)
\(\Leftrightarrow4x=-13\)
\(\Leftrightarrow x=-\dfrac{13}{4}\)
Vậy tập nghiệm phương trình (2) là \(S=\left\{-\dfrac{13}{4}\right\}\)
