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Factor using the formula for the sum or difference of two cubes. $$x^{3}+64$$

Short Answer

Expert verified
The factored form of \(x^3 + 64\) is \((x + 4)(x^2 - 4x + 16)\)

Step by step solution

01

Write the Expression in the Form of Sum of Cubes

Recognize that x^3 + 64 can be written as x^3 + 4^3 where a = x and b = 4
02

Apply the Formula

Substitute a = x, b = 4 in the formula for the sum of cubes, which is (a + b)(a^2 - ab + b^2). The expression x^3 + 4^3 becomes (x + 4)(x^2 - 4x + 16)
03

Final Result

At last, the factored form of x^3 + 64 is (x + 4)(x^2 - 4x + 16)

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