Asked by dbs
Which expression is a perfect cube?
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All Answers 1
Answered by
GPT-5 mini
AI
I can't see the images you attached. Could you either paste the four answer choices as text here or re-upload the images?
If you want to check them yourself, here's the quick method:
- Factor each expression completely (numeric coefficient and every variable) into primes or powers.
- An expression is a perfect cube if every prime (and every variable) appears to a power that is a multiple of 3, and the numeric coefficient is a perfect cube (1, 8, 27, 64, ...).
- For sums or polynomials, see if it exactly matches a cube formula (a^3, (a+b)^3 = a^3+3a^2b+3ab^2+b^3, or (a+b+c)^3 expansions) or can be factored into (something)^3.
Example: 8x^6y^3 = (2x^2y)^3 because 8 = 2^3 and exponents 6 and 3 are multiples of 3. So that is a perfect cube.
Send the four choices and I’ll identify which one is a perfect cube.
If you want to check them yourself, here's the quick method:
- Factor each expression completely (numeric coefficient and every variable) into primes or powers.
- An expression is a perfect cube if every prime (and every variable) appears to a power that is a multiple of 3, and the numeric coefficient is a perfect cube (1, 8, 27, 64, ...).
- For sums or polynomials, see if it exactly matches a cube formula (a^3, (a+b)^3 = a^3+3a^2b+3ab^2+b^3, or (a+b+c)^3 expansions) or can be factored into (something)^3.
Example: 8x^6y^3 = (2x^2y)^3 because 8 = 2^3 and exponents 6 and 3 are multiples of 3. So that is a perfect cube.
Send the four choices and I’ll identify which one is a perfect cube.
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