Carlson Vaughan
12/18/2023 · High School

\( (a x+b x)+(a y+b y) \) Determina el factor común entre los términos de cada grupo y factoriza los binomios. Primera factorización: \( x(a+b)+y(a+b) \)

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Para factorizar la expresión \( (a x+b x)+(a y+b y) \), primero identificamos los términos en cada grupo. 1. En el primer grupo \( (a x + b x) \), podemos factorizar \( x \): \[ x(a + b) \] 2. En el segundo grupo \( (a y + b y) \), podemos factorizar \( y \): \[ y(a + b) \] Ahora, juntamos ambas factorizaciones: \[ x(a + b) + y(a + b) \] Observamos que \( (a + b) \) es un factor común en ambos términos. Por lo tanto, podemos factorizarlo: \[ (a + b)(x + y) \] Así que la factorización completa de la expresión original es: \[ (a + b)(x + y) \]

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La factorización de \( (a x+b x)+(a y+b y) \) es \( (a + b)(x + y) \).
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