Have you tried expanding the expression?

Algebra Level 2

5×8 is larger than (51)×(8+1)7×12 is larger than (71)×(12+1)10×17 is larger than (101)×(17+1)\begin{aligned} 5 \times 8 &\text{ is larger than } (5-1)\times(8 + 1) \\ 7 \times 12 &\text{ is larger than } (7-1)\times(12 + 1) \\ 10 \times 17 &\text{ is larger than } (10-1)\times(17 + 1) \end{aligned}

Is it true that for all positive integers AA and BB ((with A<B),A<B), the value of A×BA\times B must be larger than (A1)×(B+1)?(A-1)\times(B+1)?

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