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Question Factor completely. \[ x^{2}-25 \] Show Examp Answer Attempt 1 out of 2 \( \square \)

Ask by Dunn King. in the United States
Feb 21,2025

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\( x^{2}-25 = (x-5)(x+5) \)

Solución

Factor the expression \( x^{2}-25 \). Factor the expression by following steps: - step0: Factor: \(x^{2}-25\) - step1: Rewrite the expression: \(x^{2}-5^{2}\) - step2: Factor the expression: \(\left(x-5\right)\left(x+5\right)\) The expression \(x^{2}-25\) can be factored as \((x-5)(x+5)\).

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Beyond the Answer

This expression is a difference of squares, which can be factored using the formula \( a^2 - b^2 = (a - b)(a + b) \). In this case, \( x^2 \) is \( a^2 \) and \( 25 \) is \( b^2 \) (since \( b = 5 \)). So, we can write the factorization as \( (x - 5)(x + 5) \). When factoring expressions like this, it’s easy to forget to check if the components can be factored further. In this case, both \( x-5 \) and \( x+5 \) are already in their simplest form, as they are linear polynomials. Always ensure each component is as simplified as possible!

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