Pregunta
Factor the biniomial completely. Select "Prime" if the polynomial cannot be factored. \( 16 m^{2}-25 n^{2}=\square \)
Ask by Tran Mccarthy. in the United States
Mar 11,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\(16m^{2}-25n^{2} = (4m-5n)(4m+5n)\)
Solución
Factor the expression \( 16m^2-25n^2 \).
Factor the expression by following steps:
- step0: Factor:
\(16m^{2}-25n^{2}\)
- step1: Rewrite the expression:
\(\left(4m\right)^{2}-\left(5n\right)^{2}\)
- step2: Factor the expression:
\(\left(4m-5n\right)\left(4m+5n\right)\)
The binomial \(16m^{2}-25n^{2}\) can be factored as \((4m-5n)(4m+5n)\).
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Simplifique esta solución Mind Expander
This expression is a difference of squares, which can be factored using the formula \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a^2 = 16m^2 \) (where \( a = 4m \)) and \( b^2 = 25n^2 \) (where \( b = 5n \)). Therefore, the expression factors to: \[ (4m - 5n)(4m + 5n) \]
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