Questions: Factor completely: 5w^3-320w = □

Transcript text: Factor completely: $5 w^{3}-320 w=$ $\square$

Solution

Solution Steps

To factor the expression $5w^3 - 320w$ completely, first identify the greatest common factor (GCF) of the terms. Then, factor out the GCF and look for any further factorization possibilities within the resulting expression.

Step 1: Identify the Expression

We start with the expression $5w^3 - 320w$.

Step 2: Factor Out the Greatest Common Factor

The greatest common factor (GCF) of the terms $5w^3$ and $-320w$ is $5w$. We factor this out: \[ 5w^3 - 320w = 5w(w^2 - 64) \]

Step 3: Further Factor the Quadratic Expression

The expression $w^2 - 64$ is a difference of squares, which can be factored as: \[ w^2 - 64 = (w - 8)(w + 8) \] Thus, we can rewrite the expression as: \[ 5w(w - 8)(w + 8) \]

Final Answer

The completely factored form of the expression $5w^3 - 320w$ is: \[ \boxed{5w(w - 8)(w + 8)} \]

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