Questions: Factor completely: u^6 - 64 y^6

Transcript text: Factor completely: \[ u^{6}-64 y^{6} \]

Solution

Step 1: Identify the Polynomial

We start with the polynomial expression given in the problem:

\[ u^{6} - 64 y^{6} \]

Step 2: Factor the Polynomial

The polynomial can be factored using the difference of squares and other algebraic identities. The factorization yields:

\[ -(-u + 2y)(u + 2y)(u^{2} - 2uy + 4y^{2})(u^{2} + 2uy + 4y^{2}) \]

Step 3: Simplify the Factorization

Rearranging the factors, we can express the factorization more clearly as:

\[ -(u - 2y)(u + 2y)(u^{2} - 2uy + 4y^{2})(u^{2} + 2uy + 4y^{2}) \]

The complete factorization of the polynomial \( u^{6} - 64 y^{6} \) is:

\[ \boxed{-(u - 2y)(u + 2y)(u^{2} - 2uy + 4y^{2})(u^{2} + 2uy + 4y^{2})} \]

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