The factored form of [tex]27\;a^{6} \; + \; 8g^{12}[/tex] is (3d² + 2g⁴)(9d⁴ - 6d²g⁴ + 4g⁸)
What is factorization?
The process of breaking down a number into smaller numbers which when multiplied together arrive at the original number.
Given that:
[tex]27\;a^{6} \; + \; 8g^{12}[/tex]
= (3)³ (a²)³ + (2)³ ([tex]g^{4}[/tex])³
= (3a²)³ + (2[tex]g^{4}[/tex])³
Now, using identity
a³+b³= (a + b)(a²-ab + b²)
= (3d² + 2g⁴)((3d²)² - 3d²2g⁴ + (2g⁴)²)
= (3d² + 2g⁴)(9d⁴ - 6d²g⁴ + 4g⁸)
Hence, the factors form is (3d² + 2g⁴)(9d⁴ - 6d²g⁴ + 4g⁸)
Learn more about factorization here:
https://brainly.com/question/2059524
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