Pena Welch
08/27/2023 · Elementary School
2) Realiza la reducción de términos semejantes en cada una de las siguientes expresiones a) \( 2 x-5 x-x+4 x-3 x-2 x+7 x \) b) \( a+2-3 a-2 a+5-6+a \) c) \( -y^{2}-8 y+2 y^{2}+3 y^{2}-5 y+2+10 y-1 \) d) \( 4 m^{2}+9+3 m^{2}+2 m+8 m-8+5 m-6 \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Para realizar la reducción de términos semejantes en cada una de las expresiones, agruparemos los términos que tienen la misma variable y luego sumaremos o restaremos sus coeficientes.
a) \( 2x - 5x - x + 4x - 3x - 2x + 7x \)
Agrupamos los términos semejantes:
\[
(2 - 5 - 1 + 4 - 3 - 2 + 7)x = (2 - 5 - 1 + 4 - 3 - 2 + 7)x = (2 - 5 - 1 + 4 - 3 - 2 + 7)x = 2x
\]
La expresión simplificada es:
\[
2x
\]
b) \( a + 2 - 3a - 2a + 5 - 6 + a \)
Agrupamos los términos semejantes:
\[
(a - 3a - 2a + a) + (2 + 5 - 6) = (-5a) + (1) = -5a + 1
\]
La expresión simplificada es:
\[
-5a + 1
\]
c) \( -y^{2} - 8y + 2y^{2} + 3y^{2} - 5y + 2 + 10y - 1 \)
Agrupamos los términos semejantes:
\[
(-y^{2} + 2y^{2} + 3y^{2}) + (-8y - 5y + 10y) + (2 - 1) = (4y^{2}) + (-3y) + (1)
\]
La expresión simplificada es:
\[
4y^{2} - 3y + 1
\]
d) \( 4m^{2} + 9 + 3m^{2} + 2m + 8m - 8 + 5m - 6 \)
Agrupamos los términos semejantes:
\[
(4m^{2} + 3m^{2}) + (2m + 8m + 5m) + (9 - 8 - 6) = (7m^{2}) + (15m) + (-5)
\]
La expresión simplificada es:
\[
7m^{2} + 15m - 5
\]
Quick Answer
a) \( 2x \)
b) \( -5a + 1 \)
c) \( 4y^{2} - 3y + 1 \)
d) \( 7m^{2} + 15m - 5 \)
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