\(\text{+)}A=1991\times1999\)
\(A=1991\times\left(1995+4\right)\)
\(A=1991\times1995+1991\times4\)
\(A=1991\times1995+7964\)
\(\text{+) }B=1995\times1995\)
\(B=\left(1991+4\right)\times1995\)
\(B=1995\times1991+1995\times4\)
\(B=1995\times1991+7980\)
\(\text{Vì 1995 x 1991 = 1991 x 1995 }\)
\(\text{Lại có :}\)
\(7964< 7980\)
\(\Rightarrow A< B\)
Giải
Ta có: \(A=1991\times1999\)
\(\Leftrightarrow A=\left(1995-4\right)\left(1995+4\right)\)
\(\Leftrightarrow A=1995\left(1995-4\right)+4\left(1995-4\right)\)
\(\Leftrightarrow A=1995^2-1995.4+4.1995-16\)
\(\Leftrightarrow A=1995^2-16\)
Vì \(1995^2-16< 1995.1995\) nên A < B
