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**INSTITUCIÓN EDUCATIVA DEPARTAMENTAL LA VICTORIA**  
**PLAN DE MEJORAMIENTO TERCER PERIODO**  
**ASIGNATURA: MATEMÁTICAS GRADO OCTAVO**  
Docente: Javier Torijano Avendaño

El siguiente plan de mejoramiento se debe realizar en hojas examen cuadriculadas en orden y con los procedimientos para cada ejercicio. La fecha de entrega es el 18 de septiembre en la hora de clase, si tiene alguna pregunta sobre los ejercicios puede realizarla en las horas de clase antes de la fecha de entrega.

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### 1. Factorizar:

a. \( a^5 - x^3 y^2 - x^5 y^2 \)  
b. \( a^5 - 3a^4 + 7a^3 \)  
c. \( 6a^2 b - 9ab^2 + 3ab \)  
d. \( 12abc + 8a^2 b^2 c + 2ab^2 c^2 \)  
e. \( -21m^2 n^2 p + 7m n^2 p + 28m n^4 p^2 \)  
f. \( 8x^7 y^5 - 16x^3 y^4 - 20x^4 y^5 \)

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### 2. Factorizar:

a. \( ax^2 + bx^2 + ay^2 + by^2 \)  
b. \( a^2 b + ab^2 + ab + 2b \)  
c. \( 18a^2 + 12a^2 - 15a - 10 \)  
d. \( a^2 + ax + a - x \)  
e. \( ab + ac + a + b \)  
f. \( m^5 n^2 - m^4 n^5 + 7m^2 - 7n^3 \)

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### 3. Factorizar:

a. \( 16x^2 - 9y^2 \)  
b. \( 144a^2 - 100b^2 \)  
c. \( 400n^2 - 169m^2 \)  
d. \( 144 - 9a^2 \)  
e. \( 121 - x^4 \)  
f. \( 4a^2 b^4 - 121 \)  
g. \( 25a^{12} - 100a^4 b^{10} \)

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### 4. Factorizar:

a. \( 8x^3 + 1 \)

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Would you like me to solve any specific exercises from this worksheet? Let me know if you need detailed solutions! 

Here are five follow-up questions to deepen your understanding:

1. What is the difference between factoring a quadratic equation and factoring a polynomial with higher-degree terms?
2. How do common factors play a role in the factoring process?
3. What is the general approach for factoring difference of squares like in question 3a and 3b?
4. Can all polynomials be factored over real numbers, or do some require complex numbers?
5. How does the distributive property help in reverse when factoring expressions?

**Tip**: Always check for common factors first when trying to factor any algebraic expression. This can simplify your work!

Factor the given algebraic expressions in the math worksheet.

This worksheet covers factoring algebraic expressions and polynomials for Grade 8 students. It includes concepts such as difference of squares, factoring by grouping, and factoring higher-degree polynomials.

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