Question
Factor the following binomial. \[ 64 x^{2}-25 \] \( ([?] x+\square)(x-\square) \)
Ask by Rogers Bartlett. in the United States
Feb 24,2025
Upstudy AI Solution
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Answer
El binomio \(64x^{2} - 25\) se factoriza como \((8x - 5)(8x + 5)\).
Solution
El binomio 64x² − 25 es una diferencia de cuadrados, ya que se puede escribir como (8x)² − (5)². Utilizando la identidad de diferencia de cuadrados, tenemos:
a² − b² = (a − b)(a + b)
Así, identificando a = 8x y b = 5, se factoriza de la siguiente manera:
64x² − 25 = (8x − 5)(8x + 5).
Esta es la factorización del binomio.
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Simplify this solution Beyond the Answer
The expression \( 64x^2 - 25 \) can be recognized as a difference of squares, which takes the form \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a = 8x \) (since \( (8x)^2 = 64x^2 \)) and \( b = 5 \) (since \( 5^2 = 25 \)). Using the difference of squares formula, we can factor it as: \[ (8x - 5)(8x + 5) \] So, you can fill in the blanks as follows: \[ (8x-5)(8x+5) \]
