Problem 57
Question
Find each product. $$(3 x-4)^{3}$$
Step-by-Step Solution
Verified Answer
The product of the expression \((3x - 4)^3\) is \(27x^3 - 108x^2 + 144x - 64\).
1Step 1: Recognize and Write Down Formula
Recognize that this problem is an example of a binomial cube and can be solved using the correct formula. The relevant formula is \((a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3\).
2Step 2: Substitute in the Values
Substitute \(a = 3x\) and \(b = 4\) into the formula. This gives \((3x - 4)^3 = (3x)^3 - 3(3x)^2*4 + 3*3x*4^2 - 4^3\).
3Step 3: Simplify the Expression
Simplify the expression to calculate the final result. This gives \(27x^3 - 108x^2 + 144x - 64\).
Other exercises in this chapter
Problem 57
Factor using the formula for the sum or difference of tho cubes. $$ x^{3}+27 $$
View solution Problem 57
Evaluate each expression or indicate that the root is not a real number. $$\sqrt[3]{-8}$$
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Add or subtract as indicated. $$\frac{4 x^{2}+x-6}{x^{2}+3 x+2}-\frac{3 x}{x+1}+\frac{5}{x+2}$$
View solution Problem 57
Simplify each exponential expression in Exercises 23–64. $$\frac{24 x^{3} y^{5}}{32 x^{7} y^{-9}}$$
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