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Answer
\(25w^{2}+20w^{3}\) factors to \(5w^{2}(5+4w)\).
Solution
Factor the expression \( 25w^{2}+20w^{3} \).
Factor the expression by following steps:
- step0: Factor:
\(25w^{2}+20w^{3}\)
- step1: Rewrite the expression:
\(5w^{2}\times 5+5w^{2}\times 4w\)
- step2: Factor the expression:
\(5w^{2}\left(5+4w\right)\)
The factored form of \(25w^{2}+20w^{3}\) is \(5w^{2}(5+4w)\).
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Simplify this solution The Deep Dive
To factor \( 25 w^{2}+20 w^{3} \), first, identify the greatest common factor (GCF) of the terms. Here, the GCF is \( 5w^{2} \). Now, factor it out: \[ 25 w^{2}+20 w^{3} = 5w^{2}(5 + 4w) \] So, the factored form is \( 5w^{2}(5 + 4w) \). If you want to double-check your work, you can expand \( 5w^{2}(5 + 4w) \) back out to verify that it returns to the original expression. This can help you catch any mistakes early and ensure you're on the right track when factoring!
