While exploring an ancient underground vault, Emek and Tara discovered a series of magical stone seals protecting a hidden historical archive. Each seal displayed a complex algebraic expression, such as products, powers, and like terms that had to be simplified correctly before the next chamber would open. Working carefully, they applied algebraic operations step by step, checking each simplification before entering it into the seal. Every correct result unlocked another passage, while incorrect work kept the doors closed. After solving the final expression, they reached the archive, preserving its priceless historical records and safely completing their expedition.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Distribute 3x^2 to every term and add the exponents of x when multiplying.
The first stone seal displays 3x^2(2x^3 - 5x + 4). Which expression is the correct simplified result?
6x^5 - 15x^3 + 12x^26x^6 - 15x^2 + 12x5x^5 - 2x^3 + 7x^26x^5 - 5x^3 + 4x^2
Correct! Distributing 3x^2 gives 6x^5 - 15x^3 + 12x^2.
Multiply both the coefficients and the powers of x in every term.
Next
🎉 Congrats! You got this question!
Hint
Simplify the expression first, then substitute x = 3.
A second seal shows the expression 2(3x - 4) - (x + 5). What is the value of the expression when x = 3?
Correct! The expression has a value of 2 when x = 3.
Distribute carefully, combine like terms, and then substitute 3 for x.
Next
🎉 Congrats! You got this question!
Hint
Apply the power to each factor in the numerator, then subtract exponents when dividing.
The final seal displays ((2a^3b^2)^2)/(4ab^3), where a and b are nonzero. Which expression correctly simplifies the seal?
a^5ba^6ba^5/b4a^5b
Correct! The expression simplifies to a^5b.
Square every factor in the numerator before dividing coefficients and subtracting exponents.
Next
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🎉 Congrats! You finished this challenge set!
Cebirsel Mühürler Kasası
TR
ARC_G12_OPS_01_STORY_01
Cebirsel Mühürler Kasası
Vault of Algebraic Seals
EN
ARC_G12_OPS_01_STORY_01
Vault of Algebraic Seals