1. The problem asks to verify if the expression $4 \times 4 - 5 \times 3$ equals 1. 2. Calculate the value: $$4 \times 4 - 5 \times 3 = 16 - 15 = 1$$ This confirms your classmate's claim for this expression. 3. Next, find the next number expression after $5 \times 5 - 6 \times 4$: Calculate the current expression: $$5 \times 5 - 6 \times 4 = 25 - 24 = 1$$ The pattern shows the first factor increasing by 1 each time, and the second factor in the second term also increasing by 1. So the next expression is: $$6 \times 6 - 7 \times 5$$ 4. To find the algebraic expression representing the set: Look at the pattern: $$2 \times 2 - 3 \times 1$$ $$3 \times 3 - 4 \times 2$$ $$4 \times 4 - 5 \times 3$$ $$5 \times 5 - 6 \times 4$$ Notice the first term is $n \times n$ and the second term is $(n+1) \times (n-1)$ where $n$ starts at 2. 5. So the algebraic expression is: $$n^2 - (n+1)(n-1)$$ 6. Simplify the expression: $$n^2 - (n+1)(n-1) = n^2 - (n^2 - 1) = n^2 - n^2 + 1 = 1$$ This matches the constant value 1 for all $n$. 7. Therefore, the correct choice is: b. $(n)(n) - [(n + 1)(n - 1)]$ 8. Here, $n$ represents the first factor in the first term of each expression, starting from 2 and increasing by 1 for each subsequent expression. Final answers: - Verification of $4 \times 4 - 5 \times 3$ equals 1. - Next expression: $6 \times 6 - 7 \times 5$ - Algebraic expression: $n^2 - (n+1)(n-1)$ - $n$ represents the starting integer in the sequence, beginning at 2.