%5E3-5.jpeg "(x-4)^3-5")
Expanding and Simplifying (x - 4)³ - 5
This expression involves both cubing a binomial and subtracting a constant. Let's break down the steps to simplify it.
Expanding the Cube
The expression (x - 4)³ represents multiplying the binomial (x - 4) by itself three times:
(x - 4)³ = (x - 4)(x - 4)(x - 4)
We can expand this step by step:
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Expand the first two factors: (x - 4)(x - 4) = x² - 8x + 16
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Multiply the result by (x - 4): (x² - 8x + 16)(x - 4) = x³ - 8x² + 16x - 4x² + 32x - 64
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Combine like terms: x³ - 12x² + 48x - 64
Simplifying the Entire Expression
Now that we've expanded (x - 4)³, we can substitute it back into the original expression:
(x - 4)³ - 5 = x³ - 12x² + 48x - 64 - 5
Finally, combine the constant terms:
x³ - 12x² + 48x - 69
Conclusion
Therefore, the simplified form of the expression (x - 4)³ - 5 is x³ - 12x² + 48x - 69. This represents a cubic polynomial, which is a polynomial with the highest power of x being 3.