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Chapter 0: Problem 58

Find each product. $$(2 x-3)^{3}$$

Short Answer

Expert verified
The product of the binomial cubed (2x-3)^3 is \(8x^3 - 36x^2 + 54x - 27\).

Step by step solution

01

Identify the binomial and its power

Here, the binomial is (2x-3) and it is raised to the power of 3.
02

Use the formula for the cube of a binomial

The formula for the cube of a binomial \(a-b\) is \(a^3 - 3a^2b + 3ab^2 - b^3\). Therefore, apply the formula on the binomial (2x-3) which means here, a = 2x and b = 3.
03

Substitute the values into the formula

Using the cube of binomial expression, the formula becomes \((2x)^3 - 3*(2x)^2*3 + 3*2x*3^2 - 3^3\) which simplifies to \(8x^3 - 3*4x^2*3 + 3*2x*9 - 27\).
04

Simplify the expression obtain the result

The product of the binomial cubed is \(8x^3 - 36x^2 + 54x - 27\).

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