Problem 59
Question
Factor using the formula for the sum or difference of two cubes. $$x^{3}+64$$
Step-by-Step Solution
Verified Answer
Hence, the factored form of \(x^3 + 64\) is \((x + 4)(x^2 - 4x + 16)\).
1Step 1: Identify a and b
In the expression \(x^3 + 64\), it can be seen that \(a = x\) and \(b = 4\), because \(64\) is the cube of \(4\). Therefore, the given expression can be rewritten as \(x^3 + 4^3\).
2Step 2: Apply the Sum of Cubes Formula
Substitute \(a = x\) and \(b = 4\) into the sum of cubes formula, which is \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\). This gives us \((x + 4)(x^2 - 4x + 16)\).
Other exercises in this chapter
Problem 58
Simplify each exponential expression. $$ \frac{10 x^{4} y^{9}}{30 x^{12} y^{-3}} $$
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simplify each complex rational expression. $$ \frac{\frac{x}{3}-1}{x-3} $$
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Evaluate each expression in Exercises \(55-66,\) or indicate that the root is not a real number. $$ \sqrt[4]{-16} $$
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In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. $$ \left(5 x^{2} y-3 x y\right)+\left(2 x^{2} y-x y\right
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