Box 1 1. Your classmate said that each of the four expressions in Box I is equivalent to 1. Verify what your classmate said by showing your computation for the number expression 4 x4-5 × 3. 2. What must be the next number expression to 5 × 5-6 × 4 in Box 1? 3. Which of the following algebraic expressions represents the set of number expressions in Box 1? a. (n)(n)(n+3)(n + 1) Number Expressions: 2x2 3x3 4×4 5x5 - 3x1 4×2 - 5x3 - 6x4 b. (n)(n)-[(n + 1)(n − 1)] c. (n-1)(n-1) - n(n-2) d. n² - 3n(1) e. n²-n-1 4. Explain or show why you think you have chosen the correct algebraic expressions for the set of number expressions in Box 1. 5. What does n represent in your chosen expression in item 3?
Answer (1)
1. Verify 4×4 – 5×3 4×4 = 16 5×3 = 15 16 – 15 = 1 So, it is equal to 1.2. Next number expression after 5×5 – 6×4 5×5 = 25 6×4 = 24 25 – 24 = 1 So, the pattern is: n×n – (n+1)×(n–1)Next will be: 6×6 – 7×53. Correct algebraic expression The pattern matches: b. (n)(n) – [(n+1)(n–1)]4. Why Because the expression shows n squared minus the product of (n+1) and (n–1). For example: n=4 → 4×4 – 5×3 → same logic.5. n represents n is the first number used for the square part.
