Pregunta
Factor the following binomial. \[ 169 x^{2}-36 y^{2} \] \( ([?] x+y)(x-\quad y) \)
Ask by Weaver Gonzalez. in the United States
Feb 21,2025
Solución de inteligencia artificial de Upstudy
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El binomio \( 169 x^{2}-36 y^{2} \) se factoriza como \( (13x-6y)(13x+6y) \).
Solución
Factor the expression by following steps:
- step0: Factor:
\(169x^{2}-36y^{2}\)
- step1: Rewrite the expression:
\(\left(13x\right)^{2}-\left(6y\right)^{2}\)
- step2: Factor the expression:
\(\left(13x-6y\right)\left(13x+6y\right)\)
El binomio \( 169 x^{2}-36 y^{2} \) se puede factorizar como:
\[
(13x-6y)(13x+6y)
\]
Por lo tanto, la respuesta es:
\[
([13] x+y)(x-6y)
\]
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Simplifique esta solución Bonus Knowledge
Did you know that the binomial \(169x^2 - 36y^2\) is a classic example of a difference of squares? The formula for factoring a difference of squares is \(a^2 - b^2 = (a - b)(a + b)\). Here, \(169x^2\) can be seen as \((13x)^2\) and \(36y^2\) as \((6y)^2\). So, this is factored as \((13x - 6y)(13x + 6y)\)! When factoring, a common mistake is to forget that both terms need to be perfect squares for the difference of squares formula to apply. Always check if both terms have integer roots or can be expressed as squares, just like we did here with \(169x^2\) and \(36y^2\). This approach will make your factoring much smoother!
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