Problem 57
Question
Factor using the formula for the sum or difference of two cubes. $$x^{3}+27$$
Step-by-Step Solution
Verified Answer
The factored form of \(x^{3}+27\) is \((x+3)\) times \((x^{2}-3x+9)\).
1Step 1: Identifying Cubes
To begin, identify the terms that can be expressed as cubes, i.e., the cube roots. In this expression, x^{3} can be written as (x)^{3} and 27 as (3)^{3}.
2Step 2: Apply the Sum of Cubes Formula
Apply the sum of cubes formula, which is \(a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2}). Hence, replace 'a' with 'x' and 'b' with '3'.
3Step 3: Final Expression
Substitute the values of 'a' and 'b' in the formula (x+3)(x^{2}-3x+9)
Other exercises in this chapter
Problem 56
Evaluate each expression in Exercises \(55-66,\) or indicate that the root is not a real number. $$\sqrt[3]{8}$$
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Rewrite each expression without absolute value bars. $$|\sqrt{5}-13|$$
View solution Problem 57
Simplify each exponential expression. $$\frac{24 x^{3} y^{3}}{32 x^{7} y^{-9}}$$
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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