At a remote mountain observatory, Emek and Tara discovered that the telescope control system had been locked by symbolic algebraic codes after a software failure. Each control panel displayed an expression that had to be simplified or rewritten into an equivalent form before the next function became available. They carefully applied algebraic identities, combined like terms, and factored expressions where appropriate, checking that each transformation preserved the original value. As the final code was accepted, the telescope aligned with its target just in time to capture a rare celestial event, restoring the observatory's mission.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Recognize the expression as a difference of two squares.
One telescope control panel displays the expression x² - 9. Which equivalent factored form should Emek and Tara enter to unlock the next function?
(x - 9)(x + 1)(x - 3)(x + 3)(x - 3)²(x + 9)(x - 1)
Correct! x² - 9 = (x - 3)(x + 3).
Review the difference of squares identity: a² - b² = (a - b)(a + b).
Next
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Hint
Distribute first, then substitute x = 4.
Another control panel shows 4(2x - 3) + 5. What is the value of the simplified expression when x = 4?
Correct! The simplified expression equals 25.
Distribute the 4 correctly, combine terms if needed, then substitute x = 4.
Next
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Hint
Multiply the coefficients and add the exponents of like bases.
The final telescope code is (3x²y)(2xy³). Which simplified expression is equivalent to this product?
5x³y⁴6x²y³6x³y⁴6x⁴y³
Correct! The product simplifies to 6x³y⁴.
Multiply coefficients first, then add exponents for x and y separately.
Next
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🎉 Congrats! You finished this challenge set!
Dağ Gözlemevi Kodları
TR
ARC_G12_OPS_01_STORY_02
Dağ Gözlemevi Kodları
Mountain Observatory Codes
EN
ARC_G12_OPS_01_STORY_02
Mountain Observatory Codes