QQuestionMathematics
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)
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