Hidden beneath an ancient mountain, Emek and Tara discovered a forgotten archive filled with sealed chambers containing valuable historical records. Each chamber was protected by a symbolic puzzle made from complex algebraic expressions. To open the locks, they simplified the expressions, transformed them into equivalent forms, and compared the results carefully. Some solutions looked correct at first but revealed hidden errors when the expressions were checked step by step. By identifying the only valid sequence of simplified results, Emek and Tara unlocked the chambers in the correct order. The recovered archive preserved the knowledge of past explorers for future generations.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Expand both products first, then combine like terms.
One archive lock displays the expression (2x - 3)(x + 5) - x(x - 4). Which simplified form should Emek and Tara verify as the correct result?
x^2 + 11x - 15x^2 + 7x - 15x^2 + 9x - 15x^2 - 11x - 15Correct! Expanding and combining terms gives x^2 + 11x - 15.
Check the multiplication of the binomials and the subtraction of the second expression.
Next🎉 Congrats! You got this question!
Hint
Substitute x = 5 after keeping track of the two operations.
A chamber puzzle contains the expression 4(2x - 1) - 3(x + 6). If x = 5, what integer value does the simplified expression produce?
Correct! The expression evaluates to 3.
Review the distribution and substitution steps carefully.
Next🎉 Congrats! You got this question!
Hint
Expand x(x + 3) before combining like terms.
Emek and Tara compare two possible solutions for an archive lock. One solution simplifies x(x + 3) + 2x to x^2 + 5x. Is this simplified form correct?
No, it should be x^2 + 3x + 2Yes, because 3x + 2x combine to 5xNo, it should be x^2 + xYes, because all terms are multiplied togetherCorrect! x(x + 3) becomes x^2 + 3x, and adding 2x gives x^2 + 5x.
Check which terms are like terms after expanding the expression.
Next🎉🎉🎉🎉🎉🎉🎉🎉
🎉 Congrats! You finished this challenge set!
