Q
QuestionMathematics

Factor using the sum or difference of two cubes formula. a^3−27
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Answer

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Step 1:
I'll solve this problem step by step using the sum or difference of cubes formula.

Step 2:
: Identify the Expression

The expression is $$a^{3} - 27

Step 3:
: Recognize the Difference of Cubes Formula

The difference of cubes formula is: $$a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})

Step 4:
: Identify the Components

- $$b = 3
In this case:

Step 5:
: Apply the Difference of Cubes Formula

a^{3} - 27 = a^{3} - 3^{3} = (a - 3)(a^{2} + 3a + 9)

Step 6:
: Verify the Factorization

- Second factor: $$a^{2} + 3a + 9
Let's check the components:

Final Answer

a^{3} - 27 = (a - 3)(a^{2} + 3a + 9)