Polynomials — Test

Question 5 • Algebra 2 with Probability

What is the factored form of 27 d to the 6th power plus 8 12th power of g ?

Answer

open paren 3 d squared plus 2 4th power of g close paren times open paren 9 d to the 4th power plus 6 d squared 4th power of g plus 4 8th power of g close paren

open paren 3 d squared plus 2 4th power of g close paren times open paren 3 d to the 4th power minus 6 d squared 4th power of g plus 2 8th power of g close paren

open paren 3 d squared plus 2 4th power of g close paren times open paren 3 d squared minus 6 d squared 4th power of g plus 2 4th power of g close paren

open paren 3 d squared plus 2 4th power of g close paren times open paren 9 d to the 4th power minus 6 d squared 4th power of g plus 4 8th power of g close paren

Explanation

Recognize 27d⁶ + 8g¹² as a sum of cubes: (3d²)³ + (2g⁴)³. Use the rule a³ + b³ = (a + b)(a² − ab + b²), giving (3d² + 2g⁴)(9d⁴ − 6d²g⁴ + 4g⁸), which is choice D.

AI-written and checked against the verified answer.

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