Problem 62
Question
Factor using the formula for the sum or difference of two cubes $$27 x^{3}-1$$
Step-by-Step Solution
Verified Answer
The factored form of the expression \(27x^3 - 1\) is \((3x - 1)(9x^2 + 3x + 1)\).
1Step 1: Identify 'a' and 'b'
In the given expression, \(27x^3\) can be rewritten as \((3x)^3\) and 1 as \(1^3\). Therefore, 'a' is 3x and 'b' is 1.
2Step 2: Apply the formula for the difference of two cubes
The difference of two cubes can be factored as: \(a^3 - b^3 = (a-b)(a^2 + ab + b^2)\). Substituting 'a' as 3x and 'b' as 1 into the formula, the expression can be factored as: (3x - 1)((3x)^2 + (3x)*1 + (1)^2).
3Step 3: Simplify the result
Simplify the resulting expression to get the final answer. This gives: (3x - 1)(9x^2 + 3x + 1).
Other exercises in this chapter
Problem 61
Evaluate each expression in Exercises \(55-66,\) or indicate that the root is not a real number. $$\sqrt[4]{(-3)^{4}}$$
View solution Problem 61
Evaluate each algebraic expression for x = 2 and y = -5. $$|x+y|$$
View solution Problem 62
Simplify each exponential expression. $$\left(\frac{-30 a^{14} b^{8}}{10 a^{17} b^{-2}}\right)^{3}$$
View solution Problem 62
Simplify each complex rational expression. $$\frac{8+\frac{1}{x}}{4-\frac{1}{x}}$$
View solution