Problem 58
Question
Find each product. $$(2 x-3)^{3}$$
Step-by-Step Solution
Verified Answer
The product of the binomial cubed (2x-3)^3 is \(8x^3 - 36x^2 + 54x - 27\).
1Step 1: Identify the binomial and its power
Here, the binomial is (2x-3) and it is raised to the power of 3.
2Step 2: 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.
3Step 3: 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 \(8x^3 - 3*4x^2*3 + 3*2x*9 - 27\).
4Step 4: Simplify the expression obtain the result
The product of the binomial cubed is \(8x^3 - 36x^2 + 54x - 27\).
Other exercises in this chapter
Problem 58
Add or subtract as indicated. $$\frac{6 x^{2}+17 x-40}{x^{2}+x-20}+\frac{3}{x-4}-\frac{5 x}{x+5}$$
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Evaluate each expression in Exercises \(55-66,\) or indicate that the root is not a real number. $$\sqrt[3]{-125}$$
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Rewrite each expression without absolute value bars. $$\frac{-7}{|-7|}$$
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Factor using the formula for the sum or difference of two cubes $$x^{3}-64$$
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