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Chapter 0: Problem 57

Find each product. $$(3 x-4)^{3}$$

Short Answer

Expert verified
The expanded form of \( (3x - 4)^3 \) is \( 27x^3 - 108x^2 + 192x - 64 \).

Step by step solution

01

Identify the binomial

The binomial given here is (3x - 4). The entire expression is raised to the power of 3.
02

Apply the cube formula

Apply the formula \( (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \) where a is 3x and b is 4. That gives us \( (3x)^3 - 3*(3x)^2*4 + 3*(3x)*4^2 - 4^3 \)
03

Compute the values

Computing the values, we get \( 27x^3 - 108x^2 + 192x - 64 \)

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Most popular questions from this chapter

Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.

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Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

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