Problem 57
Question
Find each product. $$(3 x-4)^{3}$$
Step-by-Step Solution
Verified Answer
The product is \(27x^3 - 108x^2 + 144x - 64\).
1Step 1: Identify a and b
In the given binomial \((3x -4)^3\), \(a\) is \(3x\) and \(b\) is \(4\).
2Step 2: Apply binomial theorem
We substitute \(a\) and \(b\) into the formula: \(a^3 - 3a^2b + 3ab^2 - b^3\) which gives: \((3x)^3 - 3*(3x)^2*4 + 3*3x*4^2 - 4^3\) which simplifies to: \(27x^3 - 108x^2 + 144x - 64\)
3Step 3: Confirm formula
To confirm that it was applied correctly, we can choose a random value for \(x\) and confirm that \((3x-4)^3\) equals to our derived expression.
Other exercises in this chapter
Problem 57
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
Evaluate each expression in Exercises \(55-66,\) or indicate that the root is not a real number. $$\sqrt[3]{-8}$$
View solution Problem 57
Rewrite each expression without absolute value bars. $$\frac{-3}{|-3|}$$
View solution Problem 58
Factor using the formula for the sum or difference of two cubes. $$x^{3}+64$$
View solution